A substitute for the maximum principle for singularly perturbed time-dependent semilinear reaction-diffusion problems II. Upper and lower solutions for problems with Neumann boundary conditions
- Savescu, Simona B.
2010 Mathematics Subject Classification
- 35B50 35K57 65L11 35K58 65N06
- time-dependent semilinear reaction-diffusion, singular perturbation, maximum principle (lack of), upper and lower solutions, boundary function
The boundary function method for a singularly perturbed time dependent reaction-diffusion problem with Neumann boundary conditions is modified by means of a small parameter (p) featuring in the layer functions, which allows the indication of their exponential decay rates. These functions derived by first order perturbation theory are the ingredients of upper and lower solutions providing existence of solution in the absence of a maximum principle. This solution is also unique.