Publication: Uniqueness and comparison theorems for solutions of doubly nonlinear parabolic equations with nonstandard growth conditions
Uniqueness and comparison theorems for solutions of doubly nonlinear parabolic equations with nonstandard growth conditions
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Antontsev, S., Chipot, M., & Shmarev, S. (2013). Uniqueness and comparison theorems for solutions of doubly nonlinear parabolic equations with nonstandard growth conditions. Communications on Pure and Applied Analysis, 12(4), 1527–1546. https://doi.org/10.3934/cpaa.2013.12.1527
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The paper addresses the Dirichlet problem for the doubly nonlinear parabolic equation with nonstandard growth conditions: ut = div (a(x, t, u)|u|α(x, t)|∇u|p(x, t)-2 with given variable exponents α(x, t) and p(x, t). We establish conditions on the data which guarantee the comparison principle and uniqueness of bounded weak solutions in suitable function spaces of Orlicz-Sobolev type.
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- Antontsev, Stansislav
- Chipot, Michel
- Shmarev, Sergey
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Antontsev, S., Chipot, M., & Shmarev, S. (2013). Uniqueness and comparison theorems for solutions of doubly nonlinear parabolic equations with nonstandard growth conditions. Communications on Pure and Applied Analysis, 12(4), 1527–1546. https://doi.org/10.3934/cpaa.2013.12.1527
