具有混合边界条件的非线性波方程解的适定性研究

Well-posedeness of a semilinear viscoelastic equation with mixed Dirichlet and Neumann boundary conditions

摘要: 探讨了同时具有混合边界条件和非线性边界耗散的一类非线性黏弹性波方程解的适定性．综合运用经典Galerkin逼近方法和紧性定理证明了正则解的存在唯一性；运用渐近方法优先估计并证明了广义解及弱拓扑意义下解的存在唯一性；验证了正则解、广义解和弱解关于初值的连续性．

Abstract: The well-posedness of a class of nonlinear viscoelastic wave equations with mixed boundary conditions is investigated.The existence and uniqueness of regular solutions are established through the classical Galerkin approximation method combined with the principle of compactness.A priori estimates are employed to demonstrate the well-posedness of both generalized and weak solutions.