【作者】 宋志华；

【导师】 杨志坚；

【作者基本信息】 郑州大学 ， 基础数学， 2004， 硕士

【摘要】 本文研究下列三类非线性发展方程的初边值问题的整体广义解的存在性及衰减性，其中h＞0为常数，Ω是R~N空间中有光滑边界(?)Ω的有界区域。 在第二章，利用Galerkin方法和位势井方法证明了问题(1)-(2)的整体广义解的存在性，唯一性和解的衰减性，主要结论为： 定理1假定局部Lipschitz连续。其中0≤α≤3，B(s)(s≥0)是非负连续函数。则对任意T＞0，问题(1)-(2)存在唯一的整体广义解特别，如果则广义解具有渐近性质定理2假定更多还原

【Abstract】 In this paper we study the existence and asympotic behaviour of global solutions of the initial boundary value problems for some quasilinear wave equations:where h > 0 is a constant, which has a smooth boundary is a bounded domain of RN.In Chapter 2,by constructing the potential well and applying Galerkin method,we obtain a unique global generalized solution for the problem (l)-(2).The main result is the following:Theorem 1 Suppose that(A1) f C(R2), f(s,0)s 0, s R, f(s, ) is a local Lipschitz continuous function.where 0 3, B(s) (s 0) is a nonnegative continuous function.then T > 0,the problem(l) - (2) has a unique global generalized solutionEspecially , if(A4)0< 3, |f(s,0)| B2(|s| + l) ( >, B2 >0 are real numbers),then,the generalized solution is of asymptotic propertyC* is a insertion constant from H1 to L +1,then VT > 0, the problem (l)-(2) has a unique global generalized solutionEspecially,if (A4) holds,then the generalized solution is of asymptotic property(8).In Chapter 3,by applying Galerkin method,we obtain the global generalized solution for the problem (3)-(4) under the mixed boundary conditions.By using Nakao inequality, we prove the generalized solution is of asymptotic property.The main result is the following:Theorem 3 Suppose thatEspecially , ifwhere, 1?if a > 0 , then h(t) = t1+2/; 2 if a = 0 , then h(t) = e-t, > 0,thenwhere, 1 if a > 0 , then h1(t) = t-2/; 2 if a = 0 , then h1(t) = e , 1 > 0.In Chapter 4,by constructing the potential well and applying Galerkin method,we obtain a global generalized solution for the problem (5)-(7).By using Nakao inequality, we prove the generalized solution is of asymptotic property.The main result is the following:Theorem 4 Suppose thatTheorem 5 Suppose thatwhere k = log更多还原