Cauchy problem for a class of nonlinear dispersive wave equations arising in elasto-plastic flow |
| |
Authors: | Yang Zhijian |
| |
Institution: | Department of Mathematics, Zhengzhou University, No. 75, Daxue Road, Zhengzhou 450052, PR China |
| |
Abstract: | The paper studies the existence, both locally and globally in time, stability, decay estimates and blowup of solutions to the Cauchy problem for a class of nonlinear dispersive wave equations arising in elasto-plastic flow. Under the assumption that the nonlinear term of the equations is of polynomial growth order, say α, it proves that when α>1, the Cauchy problem admits a unique local solution, which is stable and can be continued to a global solution under rather mild conditions; when α?5 and the initial data is small enough, the Cauchy problem admits a unique global solution and its norm in L1,p(R) decays at the rate for 2<p?10. And if the initial energy is negative, then under a suitable condition on the nonlinear term, the local solutions of the Cauchy problem blow up in finite time. |
| |
Keywords: | Global solution Decay estimates Blowup of solutions Nonlinear wave equation Cauchy problem |
本文献已被 ScienceDirect 等数据库收录! |
|