Mathematical Sciences: The Effects of Convection Upon the Long Time Behavior of Solutions of Reaction-Diffusion Equations

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8822788 Levine This project is to study the effects of both geometry and convective like terms on the long time behavior of solutions of reaction-diffusion equations. Questions of existence and stability of steady state solutions are also addressed. The reaction terms may appear in the transport equation or else in the flux condition on a portion of the boundary. They may be local or nonlocal functions of the solution. The geometries of interest include exterior domains and unbounded domains with unbounded complements such as cones. The nonlinear partial differential equations studied here arise in attempting to describe the behavior of physical or chemical processes. Examples include reacting flows, of interest to chemical engineers, turbulent flows, and thermoelastic materials.