Mathematical Sciences: Bifurcation from Infinity for Semilinear Elliptic PDE - The Influence of Nonlinear Growth and Domain Geometry

主要研究人员将利用无穷远分支技术研究半线性椭圆型方程解的分支的渐近行为，以获得关于这类问题解的存在性和多解性的详细信息以及相关的时间演化问题的稳定性信息。解的结构强烈依赖于空间维度和区域的几何形状。在大多数物理情况下，在存在多个解的情况下，稳态解的稳定性是极其微妙和重要的。

The principal investigators will use bifurcation from infinity techniques to study the asymptotic behavior of bifurcating branches of solutions of semilinear elliptic equations to get detailed information about the existence and multiplicity of solutions for such problems as well as stability information for the associated time-evolution problems. Solution structure is strongly dependent on the spatial dimension and the geometry of the domain. The stability of steady state solutions in the case where multiple solutions exist is extemely delicate and important in most physical situations.