一类非线性抛物型方程的边界积分公式

利用Kirchhoff积分变换将二维非线性抛物型方程化为等价的线性形式，得到该方程的边界积分方程与边界变分方程。除了利用lax—milgram定理证明变分方程解的唯一性外，还利用分段线性插值方法得到非线性系数以离散方式给出的积分变换表达式。

Boundary integral formulation for a class of nonlinear parabolic equations

By the Kirchhoff integral transformation, a class of nonlinear parabolic equations can be converted to a class of linear one, A boundary integral equation for the linear one and a boundary variational formulation are presented. In addition to the indication of existence and uniqueness of the solution of this equation using lax milgram theorem, the Kirchhoff integral transformation in the nonlinear coefficient based on a set of discrete data is given by a piece wise linear polynomial.