In this paper, existence and uniqueness of the generalized global solution and the classical global solution to the initial value problem for a class of fourth-order nonlinear wave equations are studied in the fractio...In this paper, existence and uniqueness of the generalized global solution and the classical global solution to the initial value problem for a class of fourth-order nonlinear wave equations are studied in the fractional order Sobolev space using the contraction mapping principle and the extension theorem. The sufficient conditions for the blow up of the solution to the initial value problem are given.展开更多
本文讨论非线性Klein-Gordon 方程的混合问题{u(■)—△u+u=F(u,Du,D_xDu) (t,x)∈(0,T)×Ωu(0,x)=h(x) u_t(0,x)=g(x),x∈Ω■u/■v=0■在F(u,Du,D_xDu)≥p sum from i=1 to n u_(X_i)~2+qu_t^2+u 这里(p>0,q>0) 及■_■■^...本文讨论非线性Klein-Gordon 方程的混合问题{u(■)—△u+u=F(u,Du,D_xDu) (t,x)∈(0,T)×Ωu(0,x)=h(x) u_t(0,x)=g(x),x∈Ω■u/■v=0■在F(u,Du,D_xDu)≥p sum from i=1 to n u_(X_i)~2+qu_t^2+u 这里(p>0,q>0) 及■_■■^(ph)(x)×g(x)dx>0时,得到该问题的解在有限时间内爆破.展开更多
In this article, we prove that the Cauchy problem for a N-dimensional system of nonlinear wave equations…… admits a unique global generalized solution in ……and a unique global classical solution in…… the suffici...In this article, we prove that the Cauchy problem for a N-dimensional system of nonlinear wave equations…… admits a unique global generalized solution in ……and a unique global classical solution in…… the sufficient conditions of the blow up of the solution in finite time are given, and also two examples are given.展开更多
基金supported by the National Natural Science Foundation of China (No. 10671182)
文摘In this paper, existence and uniqueness of the generalized global solution and the classical global solution to the initial value problem for a class of fourth-order nonlinear wave equations are studied in the fractional order Sobolev space using the contraction mapping principle and the extension theorem. The sufficient conditions for the blow up of the solution to the initial value problem are given.
文摘本文讨论非线性Klein-Gordon 方程的混合问题{u(■)—△u+u=F(u,Du,D_xDu) (t,x)∈(0,T)×Ωu(0,x)=h(x) u_t(0,x)=g(x),x∈Ω■u/■v=0■在F(u,Du,D_xDu)≥p sum from i=1 to n u_(X_i)~2+qu_t^2+u 这里(p>0,q>0) 及■_■■^(ph)(x)×g(x)dx>0时,得到该问题的解在有限时间内爆破.
基金supported by Tianyuan Youth Foundation of Mathematics (11226177)the National Natural Science Foundation of China (11271336 and 11171311)Foundation of He’nan Educational Committee (2009C110006)
文摘In this article, we prove that the Cauchy problem for a N-dimensional system of nonlinear wave equations…… admits a unique global generalized solution in ……and a unique global classical solution in…… the sufficient conditions of the blow up of the solution in finite time are given, and also two examples are given.
