Decay of mass for the equation \(u_t=\Delta u-a(x)u^p|\nabla u|^q\)

DOI10.1006/jdeq.2000.3771zbMath0963.35021OpenAlexW1963794767MaRDI QIDQ1587626

Ross G. Pinsky

Publication date: 18 June 2001

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.2000.3771

zbMATH Keywords

quasilinear Cauchy problemunique positive classical solvability

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Initial value problems for second-order parabolic equations (35K15)

Related Items (11)

Blow up of positive solutions for a family of nonlinear parabolic equations in general domain in \(\mathbb{R}^N\) ⋮ Global solutions and self-similar solutions of semilinear parabolic equations with nonlinear gradient terms ⋮ Positive solutions and persistence of mass for a nonautonomous equation with fractional diffusion ⋮ The Cauchy problem for \(u_{t}=\Delta u+| \nabla u|^q\) ⋮ On the growth of mass for a viscous Hamilton-Jacobi equation ⋮ The local theory for viscous Hamilton--Jacobi equations in Lebesgue spaces. ⋮ Decay of mass for fractional evolution equation with memory term ⋮ \(L^1\) decay properties for a semilinear parabolic system. ⋮ Decay of mass for nonlinear equation with fractional Laplacian ⋮ The Cauchy problem for \(u_t=\Delta u+ |\nabla u|^q\), large-time behaviour ⋮ Geometry of unbounded domains,poincaré inequalities and stability in semilinear parabolic equations

Cites Work

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• Existence and nonexistence of global solutions for \(u_ t = \Delta u + a(x)u^ p\) in \(\mathbb{R}^ d\)
• Invariant probability distributions for measure-valued diffusions.
• Global existence and decay for a nonlinear parabolic equation
• The critical measure diffusion process
• Decay of mass for a semilinear parabolic equation
• Global existence and decay for viscous Hamilton-Jacobi equations
• On the supports of measure-valued critical branching Brownian motion

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