一类非线性伪抛物型方程混合问题古典解的存在唯一性

Classical Solution to Mixed Problem for Some Nonlinear Pseudo-Parabolic Partial Equations

文章讨论了一类非线性伪抛物型方程的混合问题。首先通过积分变换,将问题的左端项简化成线性算子,然后利用该算子的Riemann函数构造一个辅助问题,得到了与原问题等价的积分微分方程,最后利用不动点理论证明了这个积分微分方程存在唯一古典解。从而得到了所述混合问题的可解性。

The aim of this paper is to investigate mixed problem for some nonlinear pseudo-parabolic partial equations. Firstly, the left side of the equation is turned into a linear operator. Then by using the Riemann's function of the operator to construct an auxiliary problem, an integrodifferential equation equivalent to former problem is obtained. Finally, based on fixed point theory, the existence and uniqueness of the classical solution to the integrodifferential equation is proved. That is, there is one and only one classical solution for the nonlinear pseudo-parabolic equation.