Spiral traveling wave solutions of nonlinear diffusion equations related to a model of spiral cyrstal growth

DOI10.2977/prims/1145476046zbMath1056.35026OpenAlexW1971385356MaRDI QIDQ1884463

Toshiko Ogiwara, Ken-Ichi Nakamura

Publication date: 1 November 2004

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1145476046

zbMATH Keywords

existenceuniquenessasymptotic stabilitytwo-dimensional annulus

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Reaction-diffusion equations (35K57) Statistical mechanics of crystals (82D25)

Related Items (3)

Towards modelling spiral motion of open plane curves ⋮ Steady State and Long Time Convergence of Spirals Moving by Forced Mean Curvature Motion ⋮ A level set approach reflecting sheet structure with single auxiliary function for evolving spirals on crystal surfaces

Cites Work

• Asymptotic behavior and stability of solutions of semilinear diffusion equations
• Geometric theory of semilinear parabolic equations
• Convergence to periodic fronts in a class of semiliner parabolic equations
• Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations
• Monotonicity and convergence results in order-preserving systems in the presence of symmetry
• Semilinear Parabolic Problems Define Semiflows on C k Spaces
• Gradient dynamics of tilted Frenkel-Kontorova models
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