Prof. Dr. Dr.h.c.mult Karl-Heinz Hoffmann
Technische Universität MünchenZentrum Mathematik - M6
Boltzmannstraße 3
85747 Garching Room: 03.04.058
Phone: +49-89-289-16802
eMail: hoffmann
ma.tum.de
Research Interests
- Approximation theory
- Optimal control theory
- Mathematical modelling of complex physical processes
- Theoretical and numerical analysis by partial differential equation
- Numerics
- Nonlinear diffusion prozesses and phase field models
Projects
- Optimal control in cryopreservation of cells and tissues, DFG Priority Program SPP 1253: Optimization with partial differential equations, Intention of Prof. K-H. Hoffmann and Dr. N.Botkin
- KAUST
Publications
2014
- A.E.Kovtanyuk, A.Yu.Chebotarev, N.D.Botkin, K.-H.Hoffmann
The unique solvability of a complex 3D heat transfer problem
Journal of Mathematical Analysis and Applications, Vol. 409 (808-815) - A.E.Kovtanyuk, A.Yu.Chebotarev, N.D.Botkin, K.-H.Hoffmann
Theoretical analysis of an optimal control problem of conductive-convective-radiative heat transfer
Journal of Mathematical Analysis and Applications, Vol. 412 (520-528) - K.-H.Hoffmann, N.D.Botkin, V.L.Turova
Models and optimal control in freezing and thawing of living cells and tissues
Trends in PDE Constrained Optimization (Int. Series of Numerical Mathematics) (155-172) - A. E. Kovtanyuk, A. Yu. Chebotarev, N. D. Botkin, K.-H. Hoffmann
Unique solvability of a steady-state complex heat transfer model
Submitted to "Communications in Nonlinear Science and Numerical Simulation" - A.E. Kovtanyuk, A.Yu.Chebotarev, N.D.Botkin, K.-H.Hoffmann
Unique solvability of a steady-state complex heat transfer model
Communications in Nonlinear Science and Numerical Simulation, 20(3) (776-784) - A.E. Kovtanyuk, A.Yu.Chebotarev, N.D.Botkin, K.-H.Hoffmann
Solvability of P1 approximation of a conductive-radiative heat transfer problem
Applied Mathematics and Computation, Vol. 249 (247-252)
2013
- N.D.Botkin, K.-H.Hoffmann, D.Marx, V.N.Starovoitov, V.L.Turova
Modeling in the development of an elasto-optical biosensor based on nanostructures
International Journal of Biomathematics and Biostatistics, Vol. 2, No. 2 (191-202) - N.D.Botkin, K.-H.Hoffmann, V.L.Turova
Mathematical modeling and simulations in cryopreservation of living cells
Edited collection "Cryopreservation: Technologies, Applications and Risks/Outcomes", Nova Science Publishers Inc (109-176) - T. G. Amler, N. D. Botkin, K.-H. Hoffmann and K. A. Ruf
Regularity of solutions of a phase field model
Dynamics of PDE, Vol.10, No.4 (353-365)
2012
- K.-H. Hoffmann, N.D. Botkin, V.L. Turova
Freezing of living cells: mathematical models and design of optimal cooling protocols
International Series of Numerical Mathematics, Vol. 160 (521-540) - A.E.Kovtanyuk, N.D.Botkin, K.-H.Hoffmann
Numerical simulations of a coupled radiative-conductive heat transfer model using a modified Monte Carlo method
International Journal of Heat and Mass Transfer 55 (649-564) - A.E.Kovtanyuk, N.D.Botkin, K.-H.Hoffmann
Numerical simulations of a coupled conductive-radiative heat transfer model
5th International Conference on High Performance Scientific Computing, March 5-9, Hanoi, Vietnam - K.-H. Hoffmann, N.D. Botkin
Multiphase flows with phase transitions: models and numerics
JP Journal of Heat and Mass Transfer, Vol. 6 (2) (73-86) - N.D.Botkin, M.Brokate, K.-H.Hoffmann, O.A.Pykhteev, V.L.Turova
Simulation of Hysteretic Effects in Multi-Phase Flows in Aquifers
AIP Conference Proceedings 1479 (1243-1246)
2011
- N.D. Botkin, K.-H. Hoffmann, V.L.Turova
Optimal control of ice formation in living cells during freezing
Applied Mathematical Modelling, Vol. 35 (4044-4057) - N.D. Botkin, K.-H. Hoffmann, V.L. Turova
Stable numerical schemes for solving Hamilton-Jacobi-Bellman-Isaacs equations
SIAM Journal on Scientific Computing, Vol. 33 (2) (992-1007) - N.D.Botkin, K.-H.Hoffmann, N.Mayer, V.L.Turova
Approximation schemes for solving disturbed control problems with non-terminal time and state constraints
Analysis, Vol. 31 (355-379)
2010
- A.E. Kovtanyuk, N.D. Botkin, K.-H. Hoffmann
Numerical simulations of a coupled conductive-radiative heat transfer model using parallel computing
Priority programm 1253 "Optimization with Partial Differential Equations", 2010 (November), Preprint-Number: SPP1253-112 (1-13) - A. Frackowiak, N.D. Botkin, M. Cialkowski, and K.-H. Hoffmann
A fitting algorithm for solving inverse problems of heat conduction
International Journal of Heat and Mass Transfer, 53 (2123-2127) - N.D. Botkin, K.-H. Hoffmann, N. Mayer, V.L. Turova
Approximation schemes for solving disturbed control problems with nonterminal time and phase constraints
Priority programm 1253 "Optimization with Partial Differential Equations", 2010 (August), Preprint-Number: SPP1253-105 (1-21) - N.D. Botkin, K.-H. Hoffmann
Optimal control in cryopreservation of living cells
Proceedings of the International Conference "Actual Problems of Stability and Control Theory" (APSCT´2009), Volume 16(5), 2010, Russia, Ekaterinburg, September 22-26 (233-240)
2009
- N.D.Botkin, K.-H.Hoffmann
Control design in cryopreservation of living cells
Abstracts of the International Conference "Actual Problems of Stability and Control Theory", September 21-26, 2009, Ekaterinburg, Russia (158-159) - T. G. Amler, N. D. Botkin, K.-H. Hoffmann, A. M. Meirmanov, V. N. Starovoitov
Transport equation with boundary conditions of hysteresis type
Mathematical Methods in the Applied Sciences, 32 (2177-2196) - N.D. Botkin, K.-H. Hoffmann, V.L.Turova
Stable solutions of Hamilton-Jacobi equations. Application to control of freezing processes.
Preprint SPP 1253-080 (1-25) - K.-H. Hoffmann, N. D. Botkin
Modeling and optimization in cryopreservation using phase field models
Abstracts of the 4th International Conference on High Performance Scientific Computing, Hanoi, Vietnam, March 2-6, 2009 (88) - N.D. Botkin, K.-H. Hoffmann, A. Frackowiak, A.M. Cialkowski
Heat exchange between air and solid surface covered with a nanostructure
submitted to International Journal of Heat and Mass Transfer
2008
- K.-H. Hoffmann, N.D. Botkin, V.L. Turova
Optimal control in cryopreservation of living tissues
Preprints of the International Conference "Differential Equations and Topology", Moscow, June 16-22, 2008 (254-255) - N.D. Botkin, K.-H. Hoffmann, A. Frackowiak, A.M. Cialkowski
Study of the heat transfer between gases and solid surfaces covered with micro rods
Preprint SPP1253-10-05, Priority programm 1253 (1-13) - N.D. Botkin, K.-H. Hoffmann, A. Frackowiak, A.M. Cialkowski
L^2 and H^(1/2) fitting algorithmus for solving inverse problems of heat transfer
Preprint SPP1253-10-06, Priority programm 1253 (1-10) - N.D. Botkin, K.-H. Hoffmann
Optimal control in cryopreservation of cells and tissues
Preprint SPP1253-10-07, Priority programm 1253 (1-34)
2007
- N.D. Botkin, K.-H. Hoffmann, O.A. Pykhteev, V.L. Turova
Dispersion relations for acoustic waves in heterogeneous multi-layered structures contacting with fluids
Journal of the Franklin Institute , Vol. 34, no. 5 (520-534) - N.D. Botkin, K.-H. Hoffmann, D. Marx
Drag on spheres in micropolar fluids with nonzero boundary conditions for microrotations
J. Fluid Mech., Vol. 590 (319-330)
2006
- N.D. Botkin, K.-H. Hoffmann, O.A. Pykhteev, B.N. Starovoitova, V.L. Turova
Two complementary approaches to modelling a biosensor
Proceedings of ASM 2006 (Applied Simulation and Modelling), June 26-28, 2006, Rhodos, Greece (525-530) - N.D. Botkin, A. M. Khludnev, K.-H. Hoffmann
The variational contact problem for elastic objects of different dimensions
Siberian Mathematical Journal, Vol. 47, no. 3 (584-593) - N.D. Botkin, H. Hölscher, M. Tewes, M. Löhndorf, K.-H. Hoffmann, E. Quandt
Modeling of pneumatic tires by a finite element model for the development a tire friction remote sensor
Computers and Structures (submitted) - K.-H. Hoffmann, V.L. Turova
Numerical simulation for microholography with short wave lengths
caesar Annual Report 2005 (Medical Technology 2_3_6) - K.-H. Hoffmann, N.D. Botkin, O.A. Pykhteev
Optimization of cooling protocols in cryopreservation of living tissues
caesar Annual Report 2005 (Biotechnology 2_2_5) - K.-H.Hoffmann, N.D.Botkin, O.A.Pykhteev
Finite element modelling of a microfluidic reaktor
caesar Annual Report 2005 (Nanotechnology/Materials Science 2_1_28) - K.-H. Hoffmann, N.D. Botkin, O.A. Pykhteev
Orthodontic film composites-superelastic composite material
caesar Annual Report 2005 (Nanotechnology/Materials Science 2_1_12) - D. Hoffmann, M. Moske, K.-H. Hoffmann, M. Giersig, R. Pascal, N. Botkin, V. Starovoitov, M. Hilgendorff, G. Treitz, M. Zabe-Kühn, B. Fassbender
ELOBIS- Elasto-optical biosensor based on nanostructures
caesar Annual Report 2005 (Biotechnology 2_2_1)
2005
- N.D. Botkin, K.-H. Hoffmann, O.A. Pykhteev, V.L. Turova
Dispersion relations for acoustic waves in heterogeneous multi-layered structures contacting with fluids
Proceedings of the First International Conference on Modeling, Simulation and Applied Optimization, February 1-3, 2005, Sharjah, U.A.E. - N.D. Botkin, K.-H. Hoffmann, V.N. Starovoitov
Homogenization of interfaces between rapidly oscillating fine elastic structures and fluids
SIAM J. Appl. Math. Vol. 65, No. 3 (983-1005) - N.D. Botkin, K.-H. Hoffmann, A.M. Meirmanov, V.N. Starovoitov
Description of adhering with saturation using boundary conditions of hysteresis type
Nonlinear Analysis 63 (1467-1473) - A. Voigt, K.-H. Hoffmann, R. Backofen, N. Botkin, A.Goepfert, O.Pykhteev, V.Turova, S.Vey, A.Zollorsch
Viola
caesar Annual Report 2004 (Nanotechnology/Materials Science 2_1_30) - K.-H.Hoffmann, N.D.Botkin, O.A.Pykhteev, V.L.Turova
MAMS: Mathematical Modeling of a Biosensor
caesar Annual Report 2004 (Coupling of Biological and Electronic Systems 2_2_1)
2004
- N.D. Botkin, K.-H. Hoffmann, O.A. Pykhteev, V.L. Turova
Numerical computation of dispersion relations for multi-layered anisotropic structures
Proceedings of the Nanotechnology conference and trade show, Boston, March 7-11, 2004 (401-414) - N.D. Botkin, K.-H. Hoffmann, F. Otto, V.N. Starovoitov, V.L. Turova
Nonlinear interaction of piezoelectrically excited surface waves
Singular Phenomena und Skaling in mathematical Models. Reinsche Fridrich-Wilhelms-Universität Bonn. Sonderforschungsbereich 611, Arbeits- und Ergebnisbericht 2002-2004 (279-303) - K.-H. Hoffmann, N.D. Botkin, O.A. Pykhteev, V.L. Turova
MAMS: Mathematical Modeling of a Biosensor
caesar Annual Report 2003 (Coupling of Biological and Electronic Systems 2_2_2)
Other years
- Chebotarev, A.Y., Grenkin, G.V., Kovtanyuk, A.E., Botkin, N.D., Hoffmann, K.-H.
Inverse problem with finite overdetermination for steady-state equations of radiative heat exchange.
Journal of Mathematical Analysis and Applications, 460., 2018 (737-744) - Chebotarev, A.Y., Grenkin, G.V., Kovtanyuk, A.E., Botkin, N.D., Hoffmann, K.-H.
Diffusion approximation of the radiative-conductive heat transfer model with Fresnel matching conditions.
Communications in Nonlinear Science and Numerical Simulation, 57., 2018 (290-298) - Kovtanyuk, A.E., Chebotarev, A.Y., Grenkin, G.V., Botkin, N.D., Hoffmann, K.-H.
Analysis of thermal processes in a multilayer biotissue exposed to optical radiation.
Proc. Int. Conf. Days on Diffraction 2017., 2017 (194-199) - G. V. Grenkin, A. Yu. Chebotarev, A. E. Kovtanyuk, N. D. Botkin, K.-H. Hoffmann.
Boundary optimal control problem of complex heat transfer model.
J. Math. Anal. Appl. 433, 2016 (1243-1260) - A. Yu. Chebotarev, A. E.Kovtanyuk, N. D.Botkin, K.-H. Hoffman.
Strong Optimal Controls in a Steady-State Problem of Complex Heat Transfer.
Submitted to the proceedings of 27 th IFIP TC7 Conference 2015, 2015 - A. Yu. Chebotarev, A. E. Kovtanyuk, G. V. Grenkin, N. D. Botkin, K.-H. Hoffmann.
Nondegeneracy of optimality conditions in control problems for a radiative-conductive heat transfer model.
Submitted to Applied Mathematics and Computation, 2015 - A.E.Kovtanyuk, A.Yu.Chebotarev, N.D.Botkin, K.-H.Hoffmann
The unique solvability of a complex 3D heat transfer problem
Journal of Mathematical Analysis and Applications, Vol. 409, 2014 (808-815) - A.E.Kovtanyuk, A.Yu.Chebotarev, N.D.Botkin, K.-H.Hoffmann
Theoretical analysis of an optimal control problem of conductive-convective-radiative heat transfer
Journal of Mathematical Analysis and Applications, Vol. 412, 2014 (520-528) - K.-H.Hoffmann, N.D.Botkin, V.L.Turova
Models and optimal control in freezing and thawing of living cells and tissues
Trends in PDE Constrained Optimization (Int. Series of Numerical Mathematics), 2014 (155-172) - A. E. Kovtanyuk, A. Yu. Chebotarev, N. D. Botkin, K.-H. Hoffmann
Unique solvability of a steady-state complex heat transfer model
Submitted to "Communications in Nonlinear Science and Numerical Simulation", 2014 - A.E. Kovtanyuk, A.Yu.Chebotarev, N.D.Botkin, K.-H.Hoffmann
Unique solvability of a steady-state complex heat transfer model
Communications in Nonlinear Science and Numerical Simulation, 20(3), 2014 (776-784) - A.E. Kovtanyuk, A.Yu.Chebotarev, N.D.Botkin, K.-H.Hoffmann
Solvability of P1 approximation of a conductive-radiative heat transfer problem
Applied Mathematics and Computation, Vol. 249, 2014 (247-252) - N.D.Botkin, K.-H.Hoffmann, D.Marx, V.N.Starovoitov, V.L.Turova
Modeling in the development of an elasto-optical biosensor based on nanostructures
International Journal of Biomathematics and Biostatistics, Vol. 2, No. 2, 2013 (191-202) - N.D.Botkin, K.-H.Hoffmann, V.L.Turova
Mathematical modeling and simulations in cryopreservation of living cells
Edited collection "Cryopreservation: Technologies, Applications and Risks/Outcomes", Nova Science Publishers Inc, 2013 (109-176) - T. G. Amler, N. D. Botkin, K.-H. Hoffmann and K. A. Ruf
Regularity of solutions of a phase field model
Dynamics of PDE, Vol.10, No.4, 2013 (353-365) - K.-H. Hoffmann, N.D. Botkin, V.L. Turova
Freezing of living cells: mathematical models and design of optimal cooling protocols
International Series of Numerical Mathematics, Vol. 160, 2012 (521-540) - A.E.Kovtanyuk, N.D.Botkin, K.-H.Hoffmann
Numerical simulations of a coupled radiative-conductive heat transfer model using a modified Monte Carlo method
International Journal of Heat and Mass Transfer 55, 2012 (649-564) - A.E.Kovtanyuk, N.D.Botkin, K.-H.Hoffmann
Numerical simulations of a coupled conductive-radiative heat transfer model
5th International Conference on High Performance Scientific Computing, March 5-9, Hanoi, Vietnam, 2012 - K.-H. Hoffmann, N.D. Botkin
Multiphase flows with phase transitions: models and numerics
JP Journal of Heat and Mass Transfer, Vol. 6 (2), 2012 (73-86) - N.D.Botkin, M.Brokate, K.-H.Hoffmann, O.A.Pykhteev, V.L.Turova
Simulation of Hysteretic Effects in Multi-Phase Flows in Aquifers
AIP Conference Proceedings 1479, 2012 (1243-1246) - N.D. Botkin, K.-H. Hoffmann, V.L.Turova
Optimal control of ice formation in living cells during freezing
Applied Mathematical Modelling, Vol. 35, 2011 (4044-4057) - N.D. Botkin, K.-H. Hoffmann, V.L. Turova
Stable numerical schemes for solving Hamilton-Jacobi-Bellman-Isaacs equations
SIAM Journal on Scientific Computing, Vol. 33 (2), 2011 (992-1007) - N.D.Botkin, K.-H.Hoffmann, N.Mayer, V.L.Turova
Approximation schemes for solving disturbed control problems with non-terminal time and state constraints
Analysis, Vol. 31, 2011 (355-379) - A.E. Kovtanyuk, N.D. Botkin, K.-H. Hoffmann
Numerical simulations of a coupled conductive-radiative heat transfer model using parallel computing
Priority programm 1253 "Optimization with Partial Differential Equations", 2010 (November), Preprint-Number: SPP1253-112, 2010 (1-13) - A. Frackowiak, N.D. Botkin, M. Cialkowski, and K.-H. Hoffmann
A fitting algorithm for solving inverse problems of heat conduction
International Journal of Heat and Mass Transfer, 53, 2010 (2123-2127) - N.D. Botkin, K.-H. Hoffmann, N. Mayer, V.L. Turova
Approximation schemes for solving disturbed control problems with nonterminal time and phase constraints
Priority programm 1253 "Optimization with Partial Differential Equations", 2010 (August), Preprint-Number: SPP1253-105, 2010 (1-21) - N.D. Botkin, K.-H. Hoffmann
Optimal control in cryopreservation of living cells
Proceedings of the International Conference "Actual Problems of Stability and Control Theory" (APSCT´2009), Volume 16(5), 2010, Russia, Ekaterinburg, September 22-26, 2010 (233-240) - N.D.Botkin, K.-H.Hoffmann
Control design in cryopreservation of living cells
Abstracts of the International Conference "Actual Problems of Stability and Control Theory", September 21-26, 2009, Ekaterinburg, Russia , 2009 (158-159) - T. G. Amler, N. D. Botkin, K.-H. Hoffmann, A. M. Meirmanov, V. N. Starovoitov
Transport equation with boundary conditions of hysteresis type
Mathematical Methods in the Applied Sciences, 32, 2009 (2177-2196) - N.D. Botkin, K.-H. Hoffmann, V.L.Turova
Stable solutions of Hamilton-Jacobi equations. Application to control of freezing processes.
Preprint SPP 1253-080, 2009 (1-25) - K.-H. Hoffmann, N. D. Botkin
Modeling and optimization in cryopreservation using phase field models
Abstracts of the 4th International Conference on High Performance Scientific Computing, Hanoi, Vietnam, March 2-6, 2009, 2009 (88) - N.D. Botkin, K.-H. Hoffmann, A. Frackowiak, A.M. Cialkowski
Heat exchange between air and solid surface covered with a nanostructure
submitted to International Journal of Heat and Mass Transfer , 2009
- K.-H. Hoffmann, N.D. Botkin, V.N. Starovoitov, V.L. Turova
Treatment of the interface between fine elastic structures and fluids with homogenization method
Preprint N100, SFB611 ``Singuläre Phänomene und Skalierung in mathematischen Modellen'', Bonn , 2003 (1-24) - N.D. Botkin, K.-H. Hoffmann, V.N. Starovoitov, V.L. Turova
Treatment of the interface between fine elastic structures and fluids
Proceedings of the International Conference ``Physics and Control'', August 20-22, 2003, St.-Petersburg , 2003 (1367-1372) - N.D. Botkin, K.-H. Hoffmann, V.N. Starovoitov, V.L. Turova
Modeling the interaction between bristle elastic structures and fluids
Proceedings of the 6th International Conference on Modeling and Simulation of Microsystems, Vol. 1, San Francisco, February 23-27, 2003 , 2003 (126-129) - N.D. Botkin, K.-H. Hoffmann, A.M. Meirmanov, V.N. Starovoitov
Diffusion problem with boundary conditions of hysteresis type
Preprint N111, SFB611 ``Singuläre Phänomene und Skalierung in mathematischen Modellen'', Bonn , 2003 (1-15) - K.-H. Hoffmann, N.D. Botkin, V.N. Starovoitov, V.L. Turova
Mathematical modeling and simulation of the biosensor
caesar Annual Report 2002 (Coupling of Biological and Electronic Systems 2_2_2), 2003 - K.-H.Hoffmann, N.D.Botkin, V.L.Turova
Biosensor: Development of Numerical Methods and Software
caesar Annual Report 2002 (Coupling of Biological and Electronic Systems 2_2_3), 2003 - N.D. Botkin, K.-H. Hoffmann
Fully coupled model of a nonlinear thin plate excited by piezoelectric actuators
Optimal control of complex structures (Oberwolfach, 2000), Internat. Ser. Numer. Math., Vol.139, Birkhäuser, Basel , 2002 (107-118) - N.D. Botkin, K.-H. Hoffmann, V.N. Starovoitov
Homogenization of interfaces between rapidly oscillating fine elastic structures and fluids
Preprint 2002-12-30 30. caesar, Bonn, 2002 - K.-H. Hoffmann, N.D. Botkin, V.L. Turova
Biosensor: Modeling and Simulation
caesar Annual Report 2001 (Coupling of Biological and Electronic Systems 2_2_2), 2002 - N.D. Botkin, K.-H. Hoffmann
Real-time optimization and stabilization of distributed parameter systems with piezoelectric elements
Online optimization of large scale systems, Springer, Berlin , 2001 (205-228) - N.D. Botkin, K.-H. Hoffmann
A fully coupled model of a nonlinear thin plate excited by piezoelectric actuators
Smart materials. Proceedings of the first caesarium (Bonn, Nov. 17-19, 1999), Springer, 2001, 2001 ( 9-22 ) - K.-H. Hoffmann, N.D. Botkin, M. Tewes, M. Schlensog, V.L. Turova
Wave propagation in biosensors
caesar Annual Report 2000 (Nanotechnology/Materials Science 2_1_3), 2001 - N.D. Botkin, K.-H. Hoffmann
Homogenization of von Kármán plates excited by piezoelectric patches
ZAMM, Vol.80, no.9 , 2000 (579-590) - N.D. Botkin, A.O. Govorov, A.V. Kalameitsev, M. Rotter, A. Wixforth, J. Kotthaus, K.-H. Hoffmann
Nonlinear acoustoelectrictransport in a two-dimensional electron system
Physical Review B, 62 (4) , 2000 (2659-2668) - N.D. Botkin, K.-H. Hoffmann
Homogenization of a fully coupled model for a nonlinear thin plate excited by piezoelectric transducers
Preprint 00-23, DFG-Project ``Echtzeit-Optimierung großer Systeme'' , 2000 (1-11) - N.D. Botkin, K.-H. Hoffmann
A fully coupled model of a nonlinear thin plate excited by piezoelectric actuators
Preprint 00-25, DFG-Project ``Echtzeit-Optimierung großer Systeme'' , 2000 (1-13)
Teaching
Past Terms
Lecture Notes
- Partial Differential Equations 1 Winter term 2005/2006, in German
- Partial Differential Equations 2 Summer term 2006, in German
