一类具曲率算子的非线性方程波前解

Traveling wavefronts for a kind of nonlinear equation with mean curvature-like operator

摘要:

本文我们考虑了以下一类具有曲率算子的非线性方程 $$\frac{\partial q(x,t)}{\partial t}+\frac{\partial}{\partial x}(\frac{\frac{\partial q(x,t)}{\partial x}}{\sqrt{1+(\frac{\partial q(x,t)}{\partial x})^{2}}})-g(q(x,t))=0.$$通过运用单调动力系统定理, 我们建立了方程波前解的存在性条件.

Abstract:

In this paper, we study the following nonlinear equation with mean curvature-like operator$$\frac{\partial q(x,t)}{\partial t}+\frac{\partial}{\partial x}(\frac{\frac{\partial q(x,t)}{\partial x}}{\sqrt{1+(\frac{\partial q(x,t)}{\partial x})^{2}}})-g( q(x,t))=0.$$ By using the theorem of the monotone dynamical system, the existence conditions of traveling wavefronts is established.