二阶椭圆和抛物型偏微分方程的非线性非局部边值问题与温控系统稳定性

本文讨论了由温度控制中提出的二阶椭圆和抛物型偏微分方程的非线性非局部边值问题.通过把问题化为变分不等方程,利用单调算子理论、凸分析和非线性发展方程理论,研究了其弱解的适定性和增长估计.证明了当反馈因(辶回)路的总增益适当小的时候,系统是全局渐近稳定的.

THE NONLINEAR AND NONLOCAL BOUNDARY VALUE PROBLEM OF THE SECOND ORDER PARTIAL DIFFERENTIAL ELLIPTIC AND PARABOLIC EQUATIONS AND THE STABILITY OF SYSTEMS OF TEMPERATURE CONTROL

The present paper is mainly concerned with the nonlinear.and nonlocal boundary value problem of the second order partial differential elliptic and parabolic equations in connection with temperature control. By turning this into a problem of variational inequalities, we have considered the well-posed and growth estimation of its weak solution, by means of monotone operator theory, convex analysis and the theory of nonlinear evolution equations. The global asymptotic stability is proved when the total gain of feedback loop is sufficiently small.