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

8822788 Levine这个项目是研究几何项和类对流项对反应扩散方程解的长时间行为的影响。文中还讨论了稳态解的存在性和稳定性问题。反应项可以出现在输运方程中，或者出现在边界的一部分上的通量条件中。它们可以是解决方案的本地函数或非本地函数。感兴趣的几何包括外部区域和具有无界补集的无界区域，如圆锥体。这里研究的非线性偏微分方程式是为了描述物理或化学过程的行为而产生的。例子包括化学工程师感兴趣的反应流、湍流流和热弹性材料。

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.