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 equation. We prove the existence of a bounded weak solution and study its localization (vanishing) properties.
CITATION STYLE
Antontsev, S., & Shmarev, S. (2007). Parabolic equations with anisotropic nonstandard growth conditions. In International Series of Numerical Mathematics (Vol. 154, pp. 33–44). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-7643-7719-9_4
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