Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6417878 | Journal of Mathematical Analysis and Applications | 2014 | 12 Pages |
Abstract
In this article, we consider the initial value problem for the equation in the title with u(x,0)=u0(x)âW21(R)â©Wâ1(R) and ut(x,0)=u1(x)âL2(R)â©Lâ(R) in the case when this equation is uniformly hyperbolic. We prove the existence and uniqueness of a local weak solution u(x,t) of this problem such that in particular (u(â ,t),ut(â ,t))â(W21(R)â©Wâ1(R))Ã(L2(R)â©Lâ(R)) for any fixed t in the interval of existence. For smooth initial data, it is proved that the life-time of the smooth solution coincides with the life-time of our weak solution.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Peter Zhidkov,