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Optimal control of electrorheological clutch described by nonlinear parabolic equation with nonlocal boundary conditions
1.  Institute of Mathematics, University of Augsburg, Universitätsstr. 14, D86159 Augsburg, Germany 
References:
[1] 
R. A. Adams, "Sobolev Spaces,", Academic Press, (1978). Google Scholar 
[2] 
J.P. Aubin, "Approximation of Elliptic BoundaryValue Problems,", Pure and Applied Mathematics, XXVI (1972). Google Scholar 
[3] 
Bayer AG, "Provisional Product Information, Rheobay TP AI 3565 and Rheobay TP AI 3566,", Bayer AG, (1260). Google Scholar 
[4] 
O. V. Besov, V. P. Il'in and S. M. Nikolsky, "Integral Representation of Functions and Embedding Theorems,", Nauka, (1975). Google Scholar 
[5] 
G. Bossis (Ed), Electrorheological Fluids and Magnetorheological suspensions,, in, (2002), 9. Google Scholar 
[6] 
P. Dreyfuss and N. Hungerbühler, Results on a NavierStokes system with applications to electrorheological fluid flow,, Int. J. Pure Appl. Math., 14 (2004), 241. Google Scholar 
[7] 
P. Dreyfuss and N. Hungerbühler, NavierStokes systems with quasimonotone viscosity tensor,, Int. J. Differ. Egu., 9 (2004), 59. Google Scholar 
[8] 
D. J. Ellam, R. J. Atkin and W. A. Bullough, Analysis of a smart clutch with cooling flow using twodimensional Bingham plastic analysis and computational fluid dynamics,, J. Power and Energy, 219 (2005), 639. Google Scholar 
[9] 
A. V. Fursikov, "Optimal Control of Distributed System. Theory and Applications,", Translated from the 1999 Russian original by Tamara Rozhkovskaya, (1999). Google Scholar 
[10] 
R. H. W. Hoppe and W. G. Litvinov, Problems on electrorheological fluid flows,, Communication on Pure and Applied Analysis, 3 (2004), 809. doi: 10.3934/cpaa.2004.3.809. Google Scholar 
[11] 
R. H. W. Hoppe, W. G. Litvinov and T. Rahman, Problems on stationary flow of electrorheological fluids in cylindrical coordinate system,, SIAM J., 65 (2005), 1633. doi: 10.1137/S0036139903432883. Google Scholar 
[12] 
V. C. L. Hutson and J. S. Pym, "Applications of Functional Analysis and Operator Theory,", Mathematics in Science and Engineering, (1980). Google Scholar 
[13] 
K. Josida, "Functional Analysis,", Springer, (1965). Google Scholar 
[14] 
L. V. Kantorovich and G. P.Akilov, "Functional Analysis,", Nauka, (1977). Google Scholar 
[15] 
O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Uraltseva, "Linear and Quasilinear Equations of Parabolic Type,", Amer. Math. Soc., (1968). Google Scholar 
[16] 
L. D. Landau and E. M. Lifschitz, "Electrodynamics of Continuous Media,", Pergamon, (1984). Google Scholar 
[17] 
J.L. Lions, "Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires,", (French) Dunod; GauthierVillars, (1969). Google Scholar 
[18] 
W. G. Litvinov, "Motion of Nonlinearly Viscous Fluid,", Nauka, (1982). Google Scholar 
[19] 
W. G. Litvinov, "Optimization in Elliptic Problems with Applications to Mechanics of Deformable Bodies and Fluid Mechanics,", Birkh\, (2000). Google Scholar 
[20] 
W. G. Litvinov, A problems on non steady flow of a nonlinear viscous fluid in a deformable pipe,, Methods of Functional Analysis and Topology, 2 (1996), 85. Google Scholar 
[21] 
W. G. Litvinov and R. H. W. Hoppe, Coupled problems on stationary nonisothermal flow of electrorheological fluids,, Com. Pure Appl. Anal., 4 (2005), 779. doi: 10.3934/cpaa.2005.4.779. Google Scholar 
[22] 
W. G. Litvinov, Problem on stationary flow of electrorheological fluids at the generalized conditions of slip on the boundary,, Com. Pure Appl. Anal., 6 (2007), 247. doi: 10.3934/cpaa.2007.6.247. Google Scholar 
[23] 
W. G. Litvinov, Dynamics of electrorheological clutch and a problem for nonlinear parabolic equation with nonlocal boundary conditions,, IMA Journal of Applied Mathematics, 73 (2008), 619. doi: 10.1093/imamat/hxn008. Google Scholar 
[24] 
G. I. Marchuk, V. I. Agoshkov, "Introduction in ProjectiveNet Methods,", Nauka, (1981). Google Scholar 
[25] 
M. Parthasarathy and D. J. Kleingenberg, Electrorheology: mechanisms and models,, Material Science and Engineering, R17 (1996), 57. Google Scholar 
[26] 
B. N. Pshenichnyi, "Necessary Optimality Conditions,", Nauka, (1969). Google Scholar 
[27] 
Y. A. Roitberg, "Elliptic Boundary Value Problems in the Spaces of Distributions,", Translated from the Russian by Peter Malyshev and Dmitry Malyshev. Mathematics and its Applications, (1996). Google Scholar 
[28] 
Z. P. Shulman and V. I. Kordonskii, "Magnetorheological Effect,", Nauka i Technika, (1982). Google Scholar 
[29] 
L. Schwartz, "Analyse Mathématique 1,", Hermann, (1967). Google Scholar 
[30] 
V. A. Solonnikov, A priori estimates for parabolic equations of the second order,, Trudy Mat. Inst. Steklov, 70 (1964), 133. Google Scholar 
[31] 
M. Whittle, R. J. Atkin and W. A. Bullough, Dynamic of a radial electrorheological clutch,, Int. J. Mod. Phys., 13 (1999), 2119. doi: 10.1142/S0217979299002216. Google Scholar 
[32] 
M. Whittle, R. J. Atkin and W. A. Bullough, Fluid dynamic limitations on the performance of an electrorheological clutch,, J. NonNewtonian Fluid Mech., 57 (1995), 61. doi: 10.1016/03770257(94)01296T. Google Scholar 
show all references
References:
[1] 
R. A. Adams, "Sobolev Spaces,", Academic Press, (1978). Google Scholar 
[2] 
J.P. Aubin, "Approximation of Elliptic BoundaryValue Problems,", Pure and Applied Mathematics, XXVI (1972). Google Scholar 
[3] 
Bayer AG, "Provisional Product Information, Rheobay TP AI 3565 and Rheobay TP AI 3566,", Bayer AG, (1260). Google Scholar 
[4] 
O. V. Besov, V. P. Il'in and S. M. Nikolsky, "Integral Representation of Functions and Embedding Theorems,", Nauka, (1975). Google Scholar 
[5] 
G. Bossis (Ed), Electrorheological Fluids and Magnetorheological suspensions,, in, (2002), 9. Google Scholar 
[6] 
P. Dreyfuss and N. Hungerbühler, Results on a NavierStokes system with applications to electrorheological fluid flow,, Int. J. Pure Appl. Math., 14 (2004), 241. Google Scholar 
[7] 
P. Dreyfuss and N. Hungerbühler, NavierStokes systems with quasimonotone viscosity tensor,, Int. J. Differ. Egu., 9 (2004), 59. Google Scholar 
[8] 
D. J. Ellam, R. J. Atkin and W. A. Bullough, Analysis of a smart clutch with cooling flow using twodimensional Bingham plastic analysis and computational fluid dynamics,, J. Power and Energy, 219 (2005), 639. Google Scholar 
[9] 
A. V. Fursikov, "Optimal Control of Distributed System. Theory and Applications,", Translated from the 1999 Russian original by Tamara Rozhkovskaya, (1999). Google Scholar 
[10] 
R. H. W. Hoppe and W. G. Litvinov, Problems on electrorheological fluid flows,, Communication on Pure and Applied Analysis, 3 (2004), 809. doi: 10.3934/cpaa.2004.3.809. Google Scholar 
[11] 
R. H. W. Hoppe, W. G. Litvinov and T. Rahman, Problems on stationary flow of electrorheological fluids in cylindrical coordinate system,, SIAM J., 65 (2005), 1633. doi: 10.1137/S0036139903432883. Google Scholar 
[12] 
V. C. L. Hutson and J. S. Pym, "Applications of Functional Analysis and Operator Theory,", Mathematics in Science and Engineering, (1980). Google Scholar 
[13] 
K. Josida, "Functional Analysis,", Springer, (1965). Google Scholar 
[14] 
L. V. Kantorovich and G. P.Akilov, "Functional Analysis,", Nauka, (1977). Google Scholar 
[15] 
O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Uraltseva, "Linear and Quasilinear Equations of Parabolic Type,", Amer. Math. Soc., (1968). Google Scholar 
[16] 
L. D. Landau and E. M. Lifschitz, "Electrodynamics of Continuous Media,", Pergamon, (1984). Google Scholar 
[17] 
J.L. Lions, "Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires,", (French) Dunod; GauthierVillars, (1969). Google Scholar 
[18] 
W. G. Litvinov, "Motion of Nonlinearly Viscous Fluid,", Nauka, (1982). Google Scholar 
[19] 
W. G. Litvinov, "Optimization in Elliptic Problems with Applications to Mechanics of Deformable Bodies and Fluid Mechanics,", Birkh\, (2000). Google Scholar 
[20] 
W. G. Litvinov, A problems on non steady flow of a nonlinear viscous fluid in a deformable pipe,, Methods of Functional Analysis and Topology, 2 (1996), 85. Google Scholar 
[21] 
W. G. Litvinov and R. H. W. Hoppe, Coupled problems on stationary nonisothermal flow of electrorheological fluids,, Com. Pure Appl. Anal., 4 (2005), 779. doi: 10.3934/cpaa.2005.4.779. Google Scholar 
[22] 
W. G. Litvinov, Problem on stationary flow of electrorheological fluids at the generalized conditions of slip on the boundary,, Com. Pure Appl. Anal., 6 (2007), 247. doi: 10.3934/cpaa.2007.6.247. Google Scholar 
[23] 
W. G. Litvinov, Dynamics of electrorheological clutch and a problem for nonlinear parabolic equation with nonlocal boundary conditions,, IMA Journal of Applied Mathematics, 73 (2008), 619. doi: 10.1093/imamat/hxn008. Google Scholar 
[24] 
G. I. Marchuk, V. I. Agoshkov, "Introduction in ProjectiveNet Methods,", Nauka, (1981). Google Scholar 
[25] 
M. Parthasarathy and D. J. Kleingenberg, Electrorheology: mechanisms and models,, Material Science and Engineering, R17 (1996), 57. Google Scholar 
[26] 
B. N. Pshenichnyi, "Necessary Optimality Conditions,", Nauka, (1969). Google Scholar 
[27] 
Y. A. Roitberg, "Elliptic Boundary Value Problems in the Spaces of Distributions,", Translated from the Russian by Peter Malyshev and Dmitry Malyshev. Mathematics and its Applications, (1996). Google Scholar 
[28] 
Z. P. Shulman and V. I. Kordonskii, "Magnetorheological Effect,", Nauka i Technika, (1982). Google Scholar 
[29] 
L. Schwartz, "Analyse Mathématique 1,", Hermann, (1967). Google Scholar 
[30] 
V. A. Solonnikov, A priori estimates for parabolic equations of the second order,, Trudy Mat. Inst. Steklov, 70 (1964), 133. Google Scholar 
[31] 
M. Whittle, R. J. Atkin and W. A. Bullough, Dynamic of a radial electrorheological clutch,, Int. J. Mod. Phys., 13 (1999), 2119. doi: 10.1142/S0217979299002216. Google Scholar 
[32] 
M. Whittle, R. J. Atkin and W. A. Bullough, Fluid dynamic limitations on the performance of an electrorheological clutch,, J. NonNewtonian Fluid Mech., 57 (1995), 61. doi: 10.1016/03770257(94)01296T. Google Scholar 
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