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
Some dependence among the Riemann functions for self-adjoint hyperbolic equations of the second order had long been studied. M. N. Olevskit considered the
In the classical embedding theorem,assume W<sub>p</sub><sup>k</sup>（R<sup>n</sup>）to be the usual Sobolev space.Ifkp【n,then W<sub>p</sub><sup>k</sup> L<...In the classical embedding theorem,assume W<sub>p</sub><sup>k</sup>（R<sup>n</sup>）to be the usual Sobolev space.Ifkp【n,then W<sub>p</sub><sup>k</sup> L<sup>q</sup>（R<sup>n</sup>）,where q<sup>-1</sup>=p<sup>-1</sup>-k/n;if kp】n,then W<sub>p</sub><sup>k</sup> L<sup>∞</sup>（R<sup>n</sup>）;in the limitingcases,if kp=n,then W<sub>p</sub><sup>k</sup> need not be in L<sup>∞</sup>（R<sup>n</sup>）.Hence,Brezis and Gallouet discoveredthe following inequality（it is called the B-G’s inequality）:展开更多
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.
文摘Some dependence among the Riemann functions for self-adjoint hyperbolic equations of the second order had long been studied. M. N. Olevskit considered the
文摘In the classical embedding theorem,assume W<sub>p</sub><sup>k</sup>（R<sup>n</sup>）to be the usual Sobolev space.Ifkp【n,then W<sub>p</sub><sup>k</sup> L<sup>q</sup>（R<sup>n</sup>）,where q<sup>-1</sup>=p<sup>-1</sup>-k/n;if kp】n,then W<sub>p</sub><sup>k</sup> L<sup>∞</sup>（R<sup>n</sup>）;in the limitingcases,if kp=n,then W<sub>p</sub><sup>k</sup> need not be in L<sup>∞</sup>（R<sup>n</sup>）.Hence,Brezis and Gallouet discoveredthe following inequality（it is called the B-G’s inequality）:
