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- W4287255790 abstract "We study the character of dependence on the data and the nonlinear structure of the equation for the solutions of the homogeneous Dirichlet problem for the evolution $p(x,t)$-Laplacian with the nonlinear source [ u_t-Delta_{p(x,t)}u=f(x,t,u),quad (x,t)in Q=Omegatimes (0,T), ] where $Omega$ is a bounded domain in $mathbb{R}^n$, $ngeq 2$, and $p(x,t)$ is a given function $p(cdot):Qmapsto (frac{2n}{n+2},p^+]$, $p^+<infty$. It is shown that the solution is stable with respect to perturbations of the variable exponent $p(x,t)$, the nonlinear source term $f(x,t,u)$, and the initial data. We obtain quantitative estimates on the norm of the difference between two solutions in a variable Sobolev space through the norms of perturbations of the nonlinearity exponent and the data $u(x,0)$, $f$. Estimates on the rate of convergence of a sequence of solutions to the solution of the limit problem are derived." @default.
- W4287255790 created "2022-07-25" @default.
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- W4287255790 date "2021-03-24" @default.
- W4287255790 modified "2023-10-17" @default.
- W4287255790 title "Stability for evolution equations with variable growth" @default.
- W4287255790 doi "https://doi.org/10.48550/arxiv.2103.13476" @default.
- W4287255790 hasPublicationYear "2021" @default.
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