Mathematical Sciences: Symmetry Methods and Nonlinear Analysis in Elastomechanics

研究者将研究微分方程， 对称性及其在固体力学中的应用 应用 涉及非线性弹性力学的几何精确公式 以及粘弹性固体和结构。 工作目标 是为了发现新的现象，并进一步开发和利用 对称性与解的节点性质之间的联系 椭圆方程，特别是在全球范围内， 分歧和延续问题。 结构弯曲的方式可以描述为 在数学上，作为描述 结构 通常弯曲取决于一个参数， 例如结构上的载荷，如果载荷变化， 结构可以在相同的负载下以不同的方式弯曲，那么 解在该载荷值处分叉。 全局描述的分叉一般很难 得到，但非常有价值。当结构对称时， 这些对称性可以用来更好地控制全球 行为 应用不仅出现在分析结构 也可以用来研究材料本身的行为。

The investigator will study differential equations with symmetry and applications to solid mechanics. The applications involve geometrically exact formulations of nonlinearly elastic and viscoelastic solids and structures. The goals of the work are to detect new phenomena and to further develop and exploit the connection between symmetry and nodal properties of solutions of elliptic equations, particularly in the context of global bifurcation and continuation problems. The way that structures bend can be described mathematically as the solution of equations describing the structure. Often the bending depends on a parameter, for instance the load on the structure, If as the load varies the structure can bend in different ways for the same load, then the solutions are said to bifurcate at that value of the load. Global descriptions of the bifurcations are generally hard to get, but are very valuable. When the structure is symmetric, those symmetries can be used to get a better grip on the global behavior. Applications arise not only in analysing structures but also in studying the behavior of materials themselves.