Mathematical Sciences: Nonlinear Problems in Classical Electromagnetic Theory

8823037 布鲁姆 这项建议是为了继续进行关于 非线性介质中的波传播及有关问题 与非线性传输线的行为相关。 数学公式涉及偏微分 方程在一个和几个维度的双曲和 混合型;兴趣在于确定 Cauchy问题解的局部和整体存在性， 初边值问题，以及结果的 解的渐近性态 还考虑了 光滑解的破裂、冲击的相关问题 形成和激波表面的存在。 许多 所呈现的模型是新的（例如，非线性波传播 超导介质与多维波传播 非平凡电导率的问题）和 有几个导致了这样的问题，其中物理参数往往 零.

8823037 Bloom This proposal is for a continuation of work on models of wave propagation in nonlinear dielectric media and on problems associated with the behavior of nonlinear transmission lines. The mathematical formulations involve partial differential equations in one and several dimensions of both hyperbolic and mixed type; the interest is in establishing results on the local and global existence of solutions to Cauchy and initial-boundary value problems, as well as results on the asymptotic behavior of solutions. Also considered are the related problems of breakdown of smooth solutions, shock formation, and the existence of shock surfaces. Many of the models presented are new (e.g., wave propagation in a nonlinear superconducting media and the multidimensional wave propagation problems in dielectrics with nontrivial conductivity) and several lead to problems in which a physical parameter tends to zero.