在二维空间中具有指数非线性项的伪抛物方程解的局部适定性

Local Well-Posedness of Solutions for Pseudo-Parabolic Equations with Exponential Nonlinearity in Two Dimensional Space

本文研究一类在二维空间中具有指数非线性项的半线性伪抛物方程Dirichlet初边值问题。借助Trudinger-Moser不等式,结合Faedo-Galerkin逼近技巧和压缩映射原理建立了问题的局部可解性。

In this paper, the Dirichlet initial boundary value problem of a semilinear pseudo-parabolic equations with exponential nonlinearity in two-dimensional space is studied. By using Trudinger-Moser inequality, Faedo-Galerkin approximation technique and contraction mapping principle, the local solvability of the problem is established.