A semilinear heat equation with initial data in negative Sobolev spaces

DOI10.3934/dcdss.2020365zbMath1458.35229OpenAlexW3024720267MaRDI QIDQ1995443

Haruki Umakoshi

Publication date: 23 February 2021

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdss.2020365

zbMATH Keywords

semilinear heat equationsingular initial data

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Initial-boundary value problems for second-order parabolic equations (35K20) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30) Semilinear parabolic equations (35K58) Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian (35K91) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (3)

Composition operators on Herz-type Triebel-Lizorkin spaces with application to semilinear parabolic equations ⋮ Solvability of a semilinear heat equation on Riemannian manifolds ⋮ Existence of solutions to fractional semilinear parabolic equations in Besov-Morrey spaces

Cites Work

• Nonlinear parabolic equations involving measures as initial conditions
• Global solutions of reaction-diffusion systems
• Critère d'existence de solutions positives pour des équations semi- linéaires non monotones. (Existence condition of positive solutions of non-monotonic semilinear equations)
• Geometric theory of semilinear parabolic equations
• Global existence of solutions to an \(n\)-dimensional parabolic-parabolic system for chemotaxis with logistic-type growth and superlinear production
• A nonlinear heat equation with singular initial data
• Non-unicité des solutions d'une équation d'évolution non-linéaire
• H ∞ Functional Calculus and Characterization of Domains of Fractional Powers
• Abstract Parabolic Evolution Equations and their Applications
• Problems paraboliques semi-lineaires avec donnees measures
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