Multiple spreading phenomena for a free boundary problem of a reaction-diffusion equation with a certain class of bistable nonlinearity

DOI10.1016/j.jde.2016.03.017zbMath1430.35277OpenAlexW2302686335MaRDI QIDQ272265

Yoshio Yamada, Yusuke Kawai

Publication date: 20 April 2016

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

Full work available at URL: https://doi.org/10.1016/j.jde.2016.03.017

zbMATH Keywords

free boundary problemreaction-diffusion equationlong time behaviorvanishingsemi-wave problemspreading

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Reaction-diffusion equations (35K57) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Nonlinear elliptic equations (35J60) Free boundary problems for PDEs (35R35) General biology and biomathematics (92B05)

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Cites Work

• Unnamed Item
• Unnamed Item
• The Stefan problem for the Fisher-KPP equation
• Spreading-vanishing dichotomy in a diffusive logistic model with a free boundary, II
• A theorem on S-shaped bifurcation curve for a positone problem with convex-concave nonlinearity and its applications to the perturbed Gelfand problem
• Relaxation oscillations in spruce-budworm interactions
• Spreading and vanishing in nonlinear diffusion problems with free boundaries
• Convergence and sharp thresholds for propagation in nonlinear diffusion problems
• Global bifurcation of steady-state solutions
• Spatial patterning of the spruce budworm
• The free boundary problem describing information diffusion in online social networks
• Spreading speed revisited: analysis of a free boundary model
• The diffusive logistic equation with a free boundary and sign-changing coefficient
• S-shaped and broken S-shaped bifurcation diagrams with hysteresis for a multiparameter spruce budworm population problem in one space dimension
• A diffusive logistic model with a free boundary in time-periodic environment
• Spreading and vanishing behaviors for radially symmetric solutions of free boundary problems for reaction-diffusion equations
• Asymptotic Behavior of Solutions to Diffusion Problems with Robin and Free Boundary Conditions
• Erratum: Spreading-Vanishing Dichotomy in the Diffusive Logistic Model with a Free Boundary
• Nonlinear Diffusion Problems with Free Boundaries: Convergence, Transition Speed, and Zero Number Arguments
• Existence and convergence to a propagating terrace in one-dimensional reaction-diffusion equations
• The zero set of a solution of a parabolic equation.
• Remarks on Spreading and Vanishing for Free Boundary Problems of Some Reaction-Diffusion Equations
• Sharp Estimate of the Spreading Speed Determined by Nonlinear Free Boundary Problems

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