一类半线性抛物型方程组解的L^∞估计

L^∞ Estimate for Solutions of Semi-linear Parobolic System

讨论来源于物理相变理论的一类半线性抛物型方程组解的一致L∞估计,该结果是利用粘性法和补偿列紧框架研究相应的双曲型守恒律解的存在性的重要内容。将V Roytburb的结果推广到非齐次情形,先对平坦函数p进行单调修正,再对修正方程组的解进行估计,最后比较原方程组的解和修正方程组解之间的关系。在方法上代替了原文正不变区域的思想,直接利用微分方程组的最大值原理解决问题。

A L^∞ bound estimate theory of phase transitions is provided on the solutions of a semi-linear parabolic system by the The existence of solutions of corresponding hyperbolic system of conservation laws is studied by viscosity methods and compensated compactness framework. V Roytburb＇ s results are generalized to inhomogeneous cases. Firstly, a monotone approximation to the flat function p is constructed, then the solutions of corresponding mudification system are estimated. Finally, the relations between the solutions of original and the modified systems are compared. Instead of positively invariant regions, the maximum principle is directly used to slove problems.