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Boundary layers in a semilinear parabolic problem.
| Content Provider | CiteSeerX |
|---|---|
| Author | Hale, Jack K. Salazar, Domingo |
| Abstract | We study a singular perturbation problem for a certain type of reaction diffusion equation with a space-dependent reaction term. We compare the effect that the presence of boundary layers versus internal layers has on the existence and stability of stationary solutions. In particular, we show that the associated eigenvalues are of different orders of magnitude for the two kinds of layers. 1 Introduction In [3], Hale and Sakamoto studied the parabolic equation u t = ffl 2 u xx + f(x; u); \Gamma1 ! x ! 1; t 0; ffl ? 0; (1) with homogeneous Neumann boundary conditions u x (\Gamma1; t) = u x (1; t) = 0: Under mild hypothesis on f and Robin Boundary conditions (see below), Zelenyak [8] proved that the !-limit set of each solution is a stationary 1991 Mathematics Subject Classification. Primary 35K57; Secondary 35B25, 35B40. solution. Hale and Sakamoto's goal was to prove the existence and determine the stability of equilibrium solutions of (1) that exhibit n internal transition lay... |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Boundary Layer Semilinear Parabolic Problem Reaction Diffusion Equation Certain Type Internal Transition Mathematics Subject Classification Parabolic Equation Limit Set Robin Boundary Condition Space-dependent Reaction Term Singular Perturbation Problem Homogeneous Neumann Boundary Condition Equilibrium Solution Different Order Internal Layer Mild Hypothesis Stationary Solution |
| Content Type | Text |
