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本文用李雅普诺夫函数法研究偏微分方程解的唯一性和稳定性,给出了关于解的唯一性的二个充分性判据,它推广了传统的能量法和文献中的有关定理,它是判断混合与初值问题解的唯一性的统一的方法。这方面的工作目前尚未见之于文献。 本文还将混合与初值间题中解对初值的连续依赖性(通常称为稳定性)推广到t→∞时的情况。引入了类似于常微分方程解的稳定性和渐近稳定性的概念,给出了判断定理,这些结果不同于。
In this paper, Lyapunov function method is used to study the uniqueness and stability of the partial differential equations. Two sufficient criteria for the uniqueness of the solution are given. It generalizes the traditional energy law and related theories in the literature. It is a unified method of judging the uniqueness of the solution to the mixed and initial value problem. Work in this area has not yet been documented. This paper also generalizes the continuous dependence of the solution on the initial value (usually called stability) to the case of t→∞. The concept of stability and asymptotical stability similar to the solution of ordinary differential equations is introduced and the judgment theorem is given. These results are different.