A free boundary problem in ecology

DOI10.1007/BF03167042zbMath0593.92019MaRDI QIDQ3724147

Yoshio Yamada, Masayasu Mimura, Shoji Yotsutani

Publication date: 1985

Published in: Japan Journal of Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

regularityasymptotic behavioruniquenessasymptotic stabilityreaction-diffusion systemomega limit setsglobal existencecomparison theoremsstationary solutionsfree boundarysemilinear parabolic equationsinteracting speciesone-dimensional habitathabitat segregation phenomenon

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Stability in context of PDEs (35B35) Population dynamics (general) (92D25) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Ecology (92D40) Free boundary problems for PDEs (35R35) Initial value problems for linear higher-order PDEs (35G10) Higher-order parabolic equations (35K25)

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Cites Work

• Remarks on the maximum principle for parabolic equations and its applications
• Some nonlinear degenerate diffusion equations related to population dynamics
• Stefan problems with the unilateral boundary condition on the fixed boundary. I
• Stefan problems with the unilateral boundary condition on the fixed boundary. II
• Stefan problems with the unilateral boundary condition on the fixed boundary. III
• Stefan problems with the unilateral boundary condition on the fixed boundary. IV
• Asymptotic behavior and stability of solutions of semilinear diffusion equations
• Geometric theory of semilinear parabolic equations
• On a certain estimate of the free boundary in the Stefan problem
• A new proof of the infinite differentiability of the free boundary in the Stefan problem
• Classical solutions of the one-dimensional, two-phase Stefan problem
• Convergence of solutions of one-dimensional semilinear parabolic equations
• A two phase Stefan problem with flux boundary conditions
• Stabilization of solutions of a degenerate nonlinear diffusion problem
• On the Existence of Weak-Solutions to an n-Dimensional Stefan Problem with Nonlinear Boundary Conditions
• Abstract Evolution Equations of Parabolic Type in Banach and Hilbert Spaces
• A strong maximum principle for parabolic equations
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