Existence of solutions for an inhomogeneous fractional semilinear heat equation

DOI10.1016/j.na.2020.111920zbMath1447.35172arXiv1910.12013OpenAlexW3025480177MaRDI QIDQ2199954

Kazuhiro Ishige, Kotaro Hisa, Jin Takahashi

Publication date: 14 September 2020

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

Full work available at URL: https://arxiv.org/abs/1910.12013

zbMATH Keywords

fractional Laplacianinhomogeneous term with singularity

Mathematics Subject Classification ID

Initial value problems for second-order parabolic equations (35K15) Semilinear parabolic equations (35K58) Fractional partial differential equations (35R11)

Related Items (5)

Existence of solutions to nonlinear parabolic equations via majorant integral kernel ⋮ Existence of solutions to fractional semilinear parabolic equations in Besov-Morrey spaces ⋮ Initial traces and solvability for a semilinear heat equation on a half space of ℝ^{ℕ} ⋮ Cauchy problem for a fractional anisotropic parabolic equation in anisotropic Hölder spaces ⋮ Solvability of superlinear fractional parabolic equations

Cites Work

• Unnamed Item
• Unnamed Item
• Heat equation with a nonlinear boundary condition and uniformly local \(L^r\) spaces
• Time-dependent singularities in semilinear parabolic equations: behavior at the singularities
• Supersolutions for a class of semilinear heat equations
• The Navier-Stokes equations with initial data in uniformly local \(L^p\) spaces.
• Some limit theorems for super-Brownian motion and semilinear differential equations
• The critical exponents for the quasi-linear parabolic equations with inhomogeneous terms
• Some observations on the Green function for the ball in the fractional Laplace framework
• Critère d'existence de solutions positives pour des équations semi- linéaires non monotones. (Existence condition of positive solutions of non-monotonic semilinear equations)
• On nonexistence of global solutions for some nonlinear integral equations
• Blow up and global existence of solutions to an inhomogeneous parabolic system
• A new critical phenomenon for semilinear parabolic problems
• Existence theorems for certain elliptic and parabolic semilinear equations
• On blow-up results for solutions of inhomogeneous evolution equations and inequalities.
• Critical exponents of Fujita type for inhomogeneous parabolic equations and systems
• Global nonexistence for the Cauchy problem of some nonlinear reaction-diffusion systems
• Existence of solutions for a fractional semilinear parabolic equation with singular initial data
• Blow-up results for nonlinear parabolic equations on manifolds
• Time-dependent singularities in semilinear parabolic equations: existence of solutions
• The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
• Estimates of heat kernel of fractional Laplacian perturbed by gradient operators
• The maximum principle and the global attractor for the dissipative 2D quasi-geostrophic equations
• Solvability of a Semilinear Parabolic Equation with Measures as Initial Data
• Qualitative properties of solutions to a time-space fractional evolution equation
• Harnack inequality for stable processes on d-sets
• Solvability of the Heat Equation with a Nonlinear Boundary Condition
• Superlinear Parabolic Problems

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