Abstract
We study the Dirichlet problem for a class of nonlinear parabolic equations with nonstandard anisotropic growth conditions. Equations of this class generalize the evolutional $p(x,t)$-Laplacian. We prove theorems of existence and uniqueness of weak solutions in suitable Orlicz-Sobolev spaces, derive global and local in time $L^{\infty}$ bounds for the weak solutions.
Citation
S. Antontsev. S. Shmarev. "Anisotropic Parabolic Equations with Variable Nonlinearity." Publ. Mat. 53 (2) 355 - 399, 2009.
Information