CONVERGENCE OF SOLUTIONS TO SOME ELLIPTIC EQUATIONS IN BOUNDED NEUMANN THIN DOMAINS

DOI10.1017/S1446788715000452zbMath1338.35151OpenAlexW2317826346MaRDI QIDQ2800024

Alessandra A. Verri, César R. de Oliveira

Publication date: 14 April 2016

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1446788715000452

zbMATH Keywords

reduction of dimensionresolvent convergencethin tubes

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Perturbation theories for operators and differential equations in quantum theory (81Q15)

Related Items (1)

On the Neumann Laplacian in nonuniformly collapsing strips

Cites Work

• Quantum singular operator limits of thin Dirichlet tubes via \(\Gamma\)-convergence
• On the spectrum and weakly effective operator for Dirichlet Laplacian in thin deformed tubes
• Asymptotic behavior of solutions of nonlinear parabolic equations on two-layer thin domains
• A remark on reaction-diffusion equations in unbounded domains
• Spectral convergence and nonlinear dynamics of reaction-diffusion equations under perturbations of the domain
• Norm resolvent convergence of Dirichlet Laplacian in unbounded thin waveguides
• Continuity of attractors for net-shaped thin domains
• Thin waveguides with Robin boundary conditions
• A General Approximation Scheme for Attractors of Abstract Parabolic Problems
• A reaction-diffusion equation on a net-shaped thin domain
• A NOTE ON RESOLVENT CONVERGENCE ON A THIN DOMAIN
• On the curvature and torsion effects in one dimensional waveguides
• The effect of domain squeezing upon the dynamics of reaction-diffusion equations

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