On the Cauchy problem for the evolution \(p\)-Laplacian equations with gradient term and source and measures as initial data

DOI10.1016/j.na.2009.12.023zbMath1184.35186OpenAlexW2029231903MaRDI QIDQ2267565

Haifeng Shang, Feng-Quan Li

Publication date: 1 March 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2009.12.023

zbMATH Keywords

nonnegative Radon measure

Mathematics Subject Classification ID

Degenerate parabolic equations (35K65) Initial value problems for second-order parabolic equations (35K15) Quasilinear parabolic equations with (p)-Laplacian (35K92)

Related Items (17)

Cauchy problem and initial traces for fast diffusion equation with space-dependent source ⋮ Singular parabolic equations with measures as initial data ⋮ The Cauchy problem for a parabolic \(p\)-Laplacian equation with combined nonlinearities ⋮ Existence of solutions for a fractional semilinear parabolic equation with singular initial data ⋮ Solvability of a semilinear heat equation on Riemannian manifolds ⋮ Critical exponents for the \(p\)-Laplace heat equations with combined nonlinearities ⋮ Local and global existence for quasilinear parabolic systems with a strongly nonlinear source ⋮ On the Cauchy problem for the singular parabolic equations with gradient term ⋮ Doubly nonlinear parabolic equations with measure data ⋮ Cauchy problem for fast diffusion equations with a gradient term ⋮ Cauchy problem for doubly nonlinear parabolic equations with initial data measures ⋮ Cauchy problem for doubly degenerate parabolic equation with gradient source ⋮ Local and global existence for evolution p-Laplacian equation with time-dependent source ⋮ Evolutionp-Laplacian equations with nonlinear source and measure data ⋮ Doubly degenerate parabolic equation with time-dependent gradient source and initial data measures ⋮ Strong solutions of forward-backward stochastic differential equations with measurable coefficients ⋮ Solvability of a Semilinear Parabolic Equation with Measures as Initial Data

Cites Work

• Degenerate parabolic equations
• On the Cauchy problem for the evolution \(p\)-Laplacian equations with gradient term and source
• Critère d'existence de solutions positives pour des équations semi- linéaires non monotones. (Existence condition of positive solutions of non-monotonic semilinear equations)
• New results on the Cauchy problem for parabolic systems and equations with strongly nonlinear sources
• Initial trace of solutions of some quasilinear parabolic equations with absorption
• Blow up of positive solutions for a family of nonlinear parabolic equations in general domain in \(\mathbb{R}^N\)
• On the Cauchy problem and initial traces for the evolution \(p\)-Laplacian equations with strongly nonlinear sources
• On the Cauchy Problem and Initial Traces for a Degenerate Parabolic Equation
• Degenerate parabolic equations with initial data measures
• Global existence and decay for viscous Hamilton-Jacobi equations
• Some Blowup Results for a Nonlinear Parabolic Equation with a Gradient Term
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