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Prof. Dr. William G. Litvinov Institut für Mathematik

# Publications:

**Publications Books.**

**Selection of the papers.**

- Optimization in Elliptic Problems with Applications to Mechanics of Deformable Bodies and Fluid Mechanics, Birkhauser, 2000, 522p.
- Optimization in Elliptic Boundary Value Problems with Applications to Mechanics, Moscow, Nauka, 1987, 366p. (in Rissian).
- Motion of Nonlinear Viscous Fluid, Moscow, Nauka, 1982, 374p. (in Russian).

- Approximation of solutions to operator equations in spaces of smooth functions and in spaces of distributions, Mum. Meth. Part. Diff. Equat. Vol. 30, Nu. , 2, 406-450, 2014
- (with T. Rahman, X.-C. Tai) A modified TV-Stokes model for image processing, SIAM J. Sci. Comput., V. 33, No. 4, pp. 1574-1597, 2011.
- Model for laminar and turbulent flows of viscous and nonlinear viscous non-Newtonianfluids. Journal of Mathematical Physics, Vol. 52, 2011, pp. 053102-1- 053102-38.
- Optimal control of electrorheological clutch described by nonlinear parabolic equation with nonlocal boundary conditions, Journal of Industrial and Management Optimization,Volume 7, Number 2, 2011, pp. 291-315.
- (with R.H.W. Hoppe) Modeling, Simulation and Optimization of Electrorheological Fluids. In P.G. Ciarlet, editors: Numerical Methods for Non-Newtonian Fluids, Vol XVI, Elsevier BV.: North Holland, 2010, pp. 719-794.
- Anisotropic model and nonstationary problem for viscoelastic polymeric fluids, Nonlinear Phenomena in Complex Systems, V. 11, No. 1, 25-39, 2008.

- Dynamics of electrorheological clutch and a problem for nonlinear parabolic equation with non-local boundary conditions, IMA Journal of Applied Mathematics, V. 73, No.3, 619-640, 2008.
- (with R.H.W. Hoppe and T. Rahman) Model of an electrorheological shock absorber and a coupled problem for partial and ordinary differential equations with variable unknown domain, European Journal of Applied Mathematics, V. 8, 513-536,2007.
- Problem on stationary flow of electrorheological fluids at the generalized conditions of slip on the boundary, Comm. Pure Appl. Anal. V. 6, No. 1, 247-277, 2007.
- (with R.H.W. Hoppe, M.Y. Kuzmin, V.G. Zvyagin) Flow of electrorheological fluid under conditions of slip on the boundary, Abst. Appl. Anal., Special Issue "Topological and Variational Methods of Nonlinear Analysis and Their Applications", 1-14, 2006.
- (with R.H.W. Hoppe) Coupled problems on stationary non-isothermal flow of electrorheological fluids, Comm. Pure Appl. Anal. V.4, No. 4., 779-803, 2005.
- (with R.H.W. Hoppe) Problems on electrorheological fluid flows, Comm.Pure Appl. Anal. V.3, No. 4., 809-848, 2004.
- Model and problem on flow of of magnetorheological fluid, Nonlinear Phenomena in Complex Systems V.7, No. 4., 332-346, 2004.
- (with R.H.W. Hoppe and T. Rahman) Problems on stationary flow of electrorheological fluids in cylindrical coordinate system, SIAM J. Appl. Math. V. 65, 1633-1656, 2005.
- (with R.H.W. Hoppe and S.J. Linz) On solutions of certain classes of evolution equations for surface morphologies, "Nonlinear Phenomena in Complex Systems", 6:1, 582-591, (2003).
- (with B. Kroeplin) Modeling and optimal control of coupled structural acoustic systems with piezoelectric elements, "Mathematical Methods in the Applied Sciences", 26/17, 1487-1516 (2003).
- A model and a general problem on plastic flow under large deformations, Z. Angew. Math. Mech. 83, 291-310 (2003).
- (with R.H.W. Hoppe) Coupled problem on non-isothermal flow of electrorheological fluid, Proceeding of 6th Congress of the Italian Society for Applied and Industrial Mathematics, Chia Laguna, May 27-31, 2002.
- (with R.H.W. Hoppe) Problem on stationary flow of electrorheological fluids under the conditions of nonhomogeneous temperature distribution, Procceding of GAMM 2002.
- General nonlocal model describing the laminar and turbulent flows of viscous and nonlinear viscous fluids and its investigation, Math. Nachr. 220, 79-110 (2000).
- (with Kroeplin, B.) Coupled problem on a shell and piezoelectric patches. (English), Ohayon, R; Bernadou, M. (ed.) 10-th International Conference Adaptive Structures and Technologies, October, 11-13, 1999, Paris, Technomic, Lancater, Basel, 475-482 (1999).
- An evolutionary problem of a flow of a nonlinear viscous fluid in a deformable viscoelastic tube. Gohberg, I. (ed.) et al., Differential and integral operators. Vol. I. Proceedings of the international workshop on operator theory and applications, IWOTA 95, Regensburg, Germany, July 31-August 4, 1995. Basel: Birkaeuser. Oper. Theory, Adv. Appl. 102, 119-129 (1998).
- Regular model and nonstationary problem for the nonlinear visco- elastic fluid. , Siberian Journal of Differential Equa- tions, 1, 351-382 (1997).
- A problem of nonsteady flow of a nonlinear viscous fluid in a deformable pipe. (English) Methods Funct. Anal. Topol. 2, No.3-4, 85-113 (1996).
- Some models and problems for laminar and turbulent flows of viscous and nonlinear viscous fluids. Z. Angew. Math. Mech. 76, Suppl. 2, 599-600 (1996).
- Some models and problems for laminar and turbulent flows of viscous and nonlinear viscous fluids. J. Math. Phys. Sci. 30, No.3, 101-157 (1996).
- (with Belonosov,M.S.) Finite element methods for nonlinearly viscous fluids. Z. Angew. Math. Mech. 76, No.6, 307-320 (1996).
- (with Panteleyev, A.D.; Sigal, V.L.; Shulman, Z.P.) On optimization of the nonsteady state temperature distribution in the local hyperthermia. Z. Angew. Math. Mech. 76, Suppl. 5, 303-304 (1996).
- On the optimal shape of a hydrofoil. J. Optimization Theory Appl. 85, No.2, 325-345 (1995).
- Problems of geometrically nonlinear elasticity. Nelineinye Granichnye Zadachi, No. 6, 72-77 (1995).
- Quasisolutions to operator equations and nonlinear problems for viscous fluids and elastic solids. Russ. J. Math. Phys. 2, No.2, 199-216 (1994).
- (with Ivanova,N.I.) Problem of the motion of a nonlinearly viscous medium in axisymmetric channels. (Russian, English) Int. Appl. Mech. 30, No.11, 906-911 (1994); translation from Prikl. Mekh., Kiev 30, No.11, 85-90 (1994).
- Optimization problems on manifolds and the shape optimization of elastic solids. Control Cybern. 23, No.3, 495-512 (1994).
- (with Krizek,M.) On the methods of penalty functions and Lagrange's multipliers in the abstract Neumann problem. Z. Angew. Math. Mech. 74, No.3, 216-218 (1994).
- Modified model of the nonlinear viscoelastic fluid and its investigation, Dyn. Syst. Appl. 2, No.4, 531-551 (1993).
- Domain shape optimization in mechanics. Control Cybern. 19, No.3/4, 203-220 (1990).
- (with Rubezhanskii, Yu. I) Convergence of solutions of problems in Timoshenko"s theory of shells to the solution of a problem in Kirchhof-Love theory. (Russian). Mat. Fiz. Nelinein. Mekh. No. 13 (47), 46-51 (1990.
- Control of the shape of the domain in elliptic systems and choice of the optimal domain in the Stokes problem. (Russian, English) Math. USSR, Sb. 67, No.1, 165-175 (1990); translation from Mat. Sb. 180, No.6, 723-732 (1989).
- (with Banichuk,N.V.;Kartvelishvili,V.M.) Optimal solutions in problems of the design of elastic plates. (Russian, English) Sov. Appl. Mech. 20, 1063-1066 (1984); translation from Prikl. Mech., Kiev 20, No.11, 82-85 (1984).
- (with Medvedev,N.G.) Splines in problems concerning the stability and strained state of rotational shells. (Russian) Vychisl. Prikl. Mat., Kiev 48, 109-113 (1982).
- Optimal control by coefficients in elliptic systems. Differ. Equations 18, 737-747 (1982).
- (with Medvedev,N.G.) Some optimal and inverse problems for orthotropic noncircular cylindrical shells. J. Optimization Theory Appl. 42, 229-246 (1984).
- (with Shishkova, N.E.) Solvability of a nonstationary problem of nonisothermal motion of a nonlinear viscous fluid with conditions of slip on the wall of a channel. (Russian), Mat. Fiz. Nelin. Mech. No 2 (36) 76-81 (1984)
- (with Medvedev,N.G.) Optimal control in problems on the stressed state of orthotropic rotational shells. (Russian) Mat. Fiz. 34, 73-77 (1983).
- (with Rubezhanskij,Yu.I.) Problems of controlling by the right-hand sides of elliptical systems and their application to control of the stress-strain state in shells. (Russian, English) J. Appl. Math. Mech. 46, 256-260 (1983); translation from Prikl. Mat. Mekh. 46, 331-336 (1982).
- Approximation of functions by tensor product of splines and of trigonometric polynomials. (Russian, English) Ukr. Math. J. 33, 196-200 (1981); translation from Ukr. Mat. Zh. 33, 252- 257 (1981).
- Optimal problems on eigenvalues. Ukr. Math. J. 33, 465-468 (1982).
- Approximation of functions by tensor product of splines and of trigonometric polynomials. (Russian, English) Ukr. Math. J. 33, 196-200 (1981); translation from Ukr. Mat. Zh. 33, 252- 257 (1981).
- (with Medvedev,N.G.) Optimal control in problems on the stressed state of orthotropic non- circular cylindric shells. (Russian) Mat. Fiz. 30, 68-74 (1981).
- Modification of the Ritz method for variational equations and its application to boundary-value problems with mixed boundary conditions. (Russian, English) Differ. Equations 17, 361-366 (1981); translation from Differ. Uravn. 17, 519-526 (1981).

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