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Uniqueness and comparison theorems for solutions of doubly nonlinear parabolic equations with nonstandard growth conditions

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  • The paper addresses the Dirichlet problem for the doubly nonlinear parabolic equation with nonstandard growth conditions: \begin{eqnarray} u_{t}=div(a(x,t,u)|u|^{\alpha(x,t)}|\nabla u|^{p(x,t)-2} \nabla u) +f(x,t) \end{eqnarray} with given variable exponents $\alpha(x,t)$ 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.
    Mathematics Subject Classification: Primary: 35K55, 35K65, 35K67.

    Citation:

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