Stationary Patterns for Reaction-Diffusion Equations.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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Patterns are defined to be stable stationary nonconstant solutions of the equations of reaction and diffusion. Several approaches are used to show the existence or nonexistence of patterns depending on one variable and defined on the entire real line. For a scalar equation, it is shown that there are essentially no patterns. For a system, small amplitude patterns, larger amplitude peaks, and larger amplitude plateaus are treated. In all cases, stability is an important consideration. Applications to ecology and biophysics are mentioned. Author
- Numerical Mathematics