Mathematical Sciences: Semilinear Partial Differential Equations and Their Applications

研究人员研究了一些化合物溶液的稳定性， Lck紧性或Liapunov反应扩散方程 泛函 这里的具体问题包括最佳条件 解的整体存在性的初始值，极限 全局解集，以及其中平衡或 行波是稳定的 他还研究点集中 无界域上椭圆型方程解的存在性 域. 集中的速度和地点是在 主要问题。 所研究的所有方程都是来自 生物学、化学或数学物理学。 更好 对这些重要方程的理解提供了对 潜在的科学问题 但是，一个彻底的研究 方程是困难的，因为缺乏通用的工具来处理 非线性方程。因此， 解决这些问题也是数学的本质。

The investigator studies stability of solutions of some reaction-diffusion equations that lck compactness or Liapunov functionals. Here specific issues include optimal conditions on the initial value for global existence of a solution, limiting sets of global solutions, and topologies in which equilibria or traveling waves are stable. He also studies point-concentration phenomena of solutions of elliptic equations in unbounded domains. The rates and locations of concentration are among the main questions. All the equations studied are model equations from biology, chemistry, or mathematical physics. Better understanding of these important equations provides insight into the underlying scientific questions. But a thorough study of the equations is difficult because of a lack of general tools to deal with nonlinear equations. Hence the problems and techniques for solving them are of intrinsic mathematical interest also.