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Exponential Asymptotics, the Viscid Burgers ' Equation, and Standing Wave Solutions for a Reaction‐Advection‐Diffusion Model
Author(s) -
Laforgue Jacques G. L.,
O'Malley, Jr. Robert E.
Publication year - 1999
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.00107
Subject(s) - mathematics , mathematical analysis , bounded function , monotonic function , exponential growth , constant (computer programming) , exponential function , nonlinear system , exponential decay , interval (graph theory) , reaction–diffusion system , advection , burgers' equation , diffusion , boundary value problem , partial differential equation , physics , thermodynamics , quantum mechanics , combinatorics , computer science , nuclear physics , programming language
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.