具周期边界的神经传播型方程的初边值问题解的存在唯一性

The Existence and Uniqueness of the Global Solutions of the Initial-Boundary Value Problem for Nerve Conduction Type Equation with Periodic Boundary

神经传播型方程的研究是非线性科学和神经科学交叉的前沿课题,既有实际应用背景,又有重要的理论意义.讨论了具周期边界的神经传播和非线性波动混合型方程的初边值问题,利用Galerkin方法及Sobolev空间理论证明了问题整体解的存在唯一性.

The study of the nerve conduction type equations is a frontier subject that cross the nonlinear science and neuroscience,in mechanics,biotechnology and other fields,it has not only the important practical background,but also great significance in theory.The initial-boundary value problem of the mixed equations of nerve conduct and nonlinear wave with periodic boundary was discussed,existence and uniqueness of the global solutions of the problem is proved by the means of Galerkin method and the theory of Sobolev space.