一类非线性强耗散发展方程的初边值问题和初值问题(英文)

INITIAL-BOUNDARY VALUE PROBLEM AND INITIAL VALUE PROBLEM FOR A CLASS OF EVOLUTION EQUATIONS WITH NONLINEAR STRONG DISSIPATION

本文研究了一类非线性强耗散发展方程(1.1)和其多维形式(3.1)具初边值打件(0.2)和(0.3)的初边值问题和初值问题.通过单调方法,紧致方法,正则化方法用它们之间的结合使用,对初边值问题,假设δ_i(s)满足(H)和(H_2)(1≤i≤4)中的任何一个,并且δ_i(s)满足(H),(H_1)',(或者(H_2)'及(H_5),我们得到(0.1)的整体强解和(3.1)的整体广义解的存在唯一性对初值问题,可得类似结果,从而Prestel的结果(1982)得到改进和推广.

In this paper we study the IBVP and the IVP for a class of evolution equations with nonlinear strong dissipation (1.1), and their multidimensional forms (4.1) with initial-boundary conditions (1.2) and (1.3) by means of the monotonicity method, the compactness method, the regularization method and their combination respectively. For the IBVP, suppose that σ_i(s) satisfy (H) and any one of (H_i) (1≤i≤4), and σ_i(s) satisfy (H)', (H_1)' (or(H_2)') and (H_5), we obtain the existence and uniqueness of the global strong solution for (1.1) and the global generalized solution for (4.1); for the IVP we obtain some similar results. So Prestel's results (1982) are improved and generalized.