Generalized Penalty and Regularization Method for Differential Variational-Hemivariational Inequalities
研究了一类含历史依赖算子和约束的微分变分-半变分不等式，证明了适定性结果，并引入无约束的惩罚和正则化问题逼近原解，最后应用于障碍抛物-椭圆系统。
<p>The primary objective of this paper is to study a large class of di erential variational-hemivariational inequalities involving history-dependent operators and constraints in a Banach space. First, we establish a well-posedness result, which includes existence, uniqueness, and continuous dependence on the initial data. Second, related penalized and regularized problems without constraints are introduced whose solutions approach the solution to the original inequality. Finally, these results are applied to an obstacle parabolic-elliptic system consisting of a nonlinear reaction-di usion equation and a time-dependent mixed boundary value problem with generalized gradient and Volterra integral terms.</p>