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Exponential Asymptotics, the Viscid Burgers ' Equation, and Standing Wave Solutions for a Reaction-Advection-Diffusion Model

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This paper studies various boundary value problems for nonlinear singularly perturbed evolutionary equations in a bounded spatial interval for all times t≥0. Under appropriate hypotheses, an O(ε)-thin monotonic profile forms that separates intervals where the solution is asymptotically constant and then moves with an exponentially slow speed toward a steady state that has an interior or endpoint layer, depending on the boundary conditions.
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Document Type: Original Article

Affiliations: 1: Universidade de Orients, Cumana, Venezuela, 2: University of Washington, Seattle, Washington

Publication date: February 1, 1999

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