GLOBAL EXISTENCE FOR A CLASS OF SYSTEMSOF NONLINEAR WAVE EQUATIONS INTHREE SPACE DIMENSIONS

作     者：S.KATAYAMA 

作者机构：Department of MathematicsWakayama University930 SakaedaniWakayama 640-8510Japan.onsider a system of nonlinear wave equationsfor i = 1 … m where F (i = 1 … m) are smooth functions of degree 2 near the origin of their arguments and u = (u1 …um) while u and x u represent the first and second derivatives of u respectively. In this paper the author presents a new class of nonlineaxity for which the global existence of small solutions is ensured. For example global existence of small solutions for arbitrary cubic termsarbitrary cubic termswill be established provided that c12 ≠c22. 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2004年第25卷第4期

页      面：463-482页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：波动方程 倍数 处处存在 偏微分方程 非线性 

摘      要：Consider a system of nonlinear wave equations (e)2t-c2i△xui=Fi(u,(e)u,(e)x(e)u) in (0,∞)×(R)3 for i=1,┈,m,where Fi(i=1,┈,m) are smooth functions of degree 2 near the origin of their arguments, and u=(u1,┈,um),while (e)u and (e)x(e)u represent the first and (second derivatives of u, respectively. In this paper, the author presents a new class of nonlinearity for which the global existence of small solutions is ensured. For example, global existence of small solutions for((e)2t- c21Δx)u1 = u2((e)tu2) + arbitrary cubic terms,((e)2t - c22Δx)u2=u1((e)tu2) + ((e)tu1)u2 + arbitrary cubic termswill be established, provided that c21 ≠ c22.