Existence and blow-up of the solution of the Cauchy problem for the generalized Rosenau equation. (Chinese. English summary) Zbl 1389.35257
Summary: This paper considers the well-posedness of solution for the Cauchy problem of the generalized damped Rosenau equation in \(\mathbf{R}\). Frist, we prove the existence and uniqueness of the local solution for the problem by the contraction mapping principle. Then the existence of the global solution of the problem is proved. Finally, we study the blow-up of the solution for the problem by concavity method.
MSC:
35Q35 | PDEs in connection with fluid mechanics |
35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
35B44 | Blow-up in context of PDEs |