An Asymptotic Analysis of Localized Solutions for Some Reaction‐Diffusion Models in Multidimensional Domains
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Publication:4895085
DOI10.1002/sapm1996972103zbMath0932.35059OpenAlexW1206136296MaRDI QIDQ4895085
Publication date: 13 October 1996
Published in: Studies in Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/sapm1996972103
Bratu's equationspectral resultsspike-layer solutionexponentially small eigenvalueshot-spot solutionslimiting solvability condition
Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)
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Cites Work
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- Semilinear elliptic singular perturbation problems with nonuniform interior behavior
- Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
- Locating the peaks of least-energy solutions to a semilinear Neumann problem
- On the motion of viscous shocks and the supersensitivity of their steady- state limits
- Asymptotic Solutions for a Dirichlet Problem with an Exponential Nonlinearity
- On Spurious Solutions of Singular Perturbation Problems
- A Variational Approach to Nonlinear Singularly Perturbed Boundary-Value Problems
- On the shape of least‐energy solutions to a semilinear Neumann problem
- Eliminating Indeterminacy in Singularly Perturbed Boundary Value Problems with Translation Invariant Potentials
- The Exit Problem for Randomly Perturbed Dynamical Systems
- Slow dynamics for the cahn-hilliard equation in higher space dimension part i: spectral estimates∗
- Metastable Bubble Solutions for the Allen-Cahn Equation with Mass Conservation
