Unique solvability of initial boundary value problems for anisotropic elliptic-parabolic equations with variable exponents of nonlinearity
M. M. Bokalo, O. M. Buhrii
Department of Differential Equations, Faculty of Mechanics and Mathematics, Ivan Franko National University of Lviv ; 79000-Lviv, Ukraine
R. A. Mashiyev
Department of Mathematics, Faculty of Science, Dicle University ; 21280-Diyarbakir, Turkey
Received on November 13, 2012, revised version on January 17, 2013
Accepted on January 31, 2013
Communicated by Alexander Pankov
| Abstract. Existence and uniqueness of weak solutions of initial-boundary-value problems for second order elliptic-parabolic equations are proved.These equations have the exponents of nonlinearity depending on the points of domain and the direction of differentiation. The weak solutions belong to some generalized Sobolev spaces. | |
| Keywords: | nonlinear equation, anisotropic equation, elliptic-parabolic equation, degenerate parabolic equation, initial-boundary-value problem, variable exponents of nonlinearity, generalized Lebesgue space, generalized Sobolev space. |
| 2010 Mathematics Subject Classification: 35D05, 35J25, 35J60, 35K15, 35K55. | |