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- W4285178281 abstract "We study the Dirichlet problem for the degenerate parabolic equation of the Kirchhoff type [ u_{t}-aleft( u _{L^{p}(Omega)}^{p}right)sumlimits_{i=1}^{n}D_{i}left( leftvert urightvert ^{p-2}D_{i}uright) +bleft( x,t,uright)=fleft( x,tright) quad text{in $Q_T=Omega times (0,T)$}, ] where $pgeq2$, $T>0$, $Omega subset mathbb{R}^{n}$, $ngeq 2$, is a smooth bounded domain. The coefficient $a(cdot)$ is real-valued function defined on $mathbb{R}_+$ and $b(cdot,cdot,tau)$ is a measurable function with variable nonlinearity in $tau$. We prove existence of weak solutions of the considered problem under appropriate and general conditions on $a$ and $b$. Sufficient conditions for uniqueness are found and in the case $fequiv0$ the decay rates for $ u _{L^2(Omega)}$ are obtained." @default.
- W4285178281 created "2022-07-14" @default.
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- W4285178281 date "2022-01-01" @default.
- W4285178281 modified "2023-10-13" @default.
- W4285178281 title "On a class of nonlocal porous medium equations of Kirchhoff type" @default.
- W4285178281 doi "https://doi.org/10.55730/1300-0098.3265" @default.
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