Semilinear elliptic equations on thin network-shaped domains with variable thickness

DOI10.1006/jdeq.2001.4119zbMath1010.35032OpenAlexW2040908826MaRDI QIDQ697864

Satoshi Kosugi

Publication date: 17 September 2002

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

Full work available at URL: https://doi.org/10.1006/jdeq.2001.4119

zbMATH Keywords

asymptotic behaviourgeometric graphscomparison technique

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Boundary value problems for second-order elliptic equations (35J25) Nonlinear elliptic equations (35J60) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items (5)

Error estimate for classical solutions to the heat equation in a moving thin domain and its limit equation ⋮ Spectral stability of shifted states on star graphs ⋮ Spectral properties of Schrödinger operators on radial \(N\)-dimensional infinite trees ⋮ Diffusion processes in thin tubes and their limits on graphs ⋮ Approximations of metric graphs by thick graphs and their Laplacians

Cites Work

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• Singular perturbation of domains and the semilinear elliptic equation. II
• A semilinear elliptic equation in a thin network-shaped domain
• Existence of stable stationary solutions of scalar reaction-diffusion equations in thin tubular domains
• Elliptic Partial Differential Equations of Second Order
• A reaction-diffusion equation on a thin L-shaped domain
• Stability of nonconstant steady states in reaction-diffusion systems on graphs

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