Asymptotic Profiles of Solutions and Propagating Terrace for a Free Boundary Problem of Nonlinear Diffusion Equation with Positive Bistable Nonlinearity

DOI10.1137/18M1209970zbMath1452.35261OpenAlexW2999936151WikidataQ111174003 ScholiaQ111174003MaRDI QIDQ5208766

Yuki Kaneko, Hiroshi Matsuzawa, Yoshio Yamada

Publication date: 10 January 2020

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/18m1209970

zbMATH Keywords

one space dimensionspreading solution

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order parabolic equations (35K20) Free boundary problems for PDEs (35R35) Semilinear parabolic equations (35K58)

Related Items (12)

Approximation of random diffusion equations by nonlocal diffusion equations in free boundary problems of one space dimension ⋮ A free boundary problem of nonlinear diffusion equation with positive bistable nonlinearity in high space dimensions. I: Classification of asymptotic behavior ⋮ Propagation and reaction–diffusion models with free boundaries ⋮ Unnamed Item ⋮ Asymptotic behavior of spreading fronts in an anisotropic multi-stable equation on \(\mathbb{R}^N\) ⋮ A free boundary problem of nonlinear diffusion equation with positive bistable nonlinearity in high space dimensions. II: Asymptotic profiles of solutions and radial terrace solution ⋮ Propagation, diffusion and free boundaries ⋮ Semi-wave and spreading speed of the nonlocal Fisher-KPP equation with free boundaries ⋮ Long-time dynamics of a diffusive epidemic model with free boundaries ⋮ Spreading speed for some cooperative systems with nonlocal diffusion and free boundaries. I: Semi-wave and a threshold condition ⋮ Free boundary problem for a reaction-diffusion equation with positive bistable nonlinearity ⋮ Spreading under shifting climate by a free boundary model: Invasion of deteriorated environment

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