Non-Linear Partial Differential Equations —— An Algebraic View of Generalized Solutions

----- 非线性偏微分方程：广义解的代数视图

ISBN: 9780444887009 出版年：1990 页码：403 Rosinger, E E North Holland_RM

A massive transition of interest from solving linear partial differential equations to solving nonlinear ones has taken place during the last two or three decades. The availability of better computers has often made numerical experimentations progress faster than the theoretical understanding of nonlinear partial differential equations. The three most important nonlinear phenomena observed so far both experimentally and numerically, and studied theoretically in connection with such equations have been the solitons, shock waves and turbulence or chaotical processes. In many ways, these phenomena have presented increasing difficulties in the mentioned order. In particular, the latter two phenomena necessarily lead to nonclassical or generalized solutions for nonlinear partial differential equations.