Blow-up for a Porous Medium Equation with Local Linear Boundary Dissipation
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DOI: 10.1051/wujns/2024292095
Abstract: This article investigates the blow-up behaviors for a porous medium equation with a superlinear source and local linear boundary dissipation. Making use of the concavity method, we establish sufficient conditions to guarantee the occurrence of… read more here.
Keywords: local linear; linear boundary; medium equation; porous medium ... See more keywords
Second-Order Gradient Estimates for the Porous Medium Equation on Riemannian Manifolds
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DOI: 10.3390/math13101683
Abstract: In this paper, we derive second-order gradient estimates for positive solutions of the porous medium equation ∂∂tu(x,t)=Δu(x,t)p,p∈1,1+1n−1 on an n-dimensional Riemannian manifold under certain curvature conditions. read more here.
Keywords: gradient estimates; medium equation; porous medium; order gradient ... See more keywords
Local Aronson-Bénilan gradient estimates and Harnack inequality for the porous medium equation along Ricci flow
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DOI: 10.3934/cpaa.2018093
Abstract: In this paper, we prove some new local Aronson-Benilan type gradient estimates for positive solutions of the porous medium equation \begin{document}$u_{t}=Δ u^{m}, m>1$ \end{document} coupled with Ricci flow, assuming that the Ricci curvature is bounded.… read more here.
Keywords: gradient estimates; harnack inequality; local aronson; ricci flow ... See more keywords