Lifespan estimates for wave equations with damping and potential posed on asymptotically Euclidean manifolds

Mengyun Liu

Lifespan estimates for wave equations with damping and potential posed on asymptotically Euclidean manifolds

Analysis of PDEs 2021-04-21 v2

Authors: Mengyun Liu

Abstract

In this work, we investigate the problem of finite time blow up as well as the upper bound estimates of lifespan for solutions to small-amplitude semilinear wave equations with time dependent damping and potential, and mixed nonlinearities $c_1 |u_t|^p+c_2 |u|^q$ , posed on asymptotically Euclidean manifolds, which is related to both the Strauss conjecture and the Glassey conjecture.

Keywords

wave equation lifespan estimate damping potential asymptotically euclidean manifold strauss conjecture glassey conjecture

Cite

@article{arxiv.2104.08497,
  title  = {Lifespan estimates for wave equations with damping and potential posed on asymptotically Euclidean manifolds},
  author = {Mengyun Liu},
  journal= {arXiv preprint arXiv:2104.08497},
  year   = {2021}
}

Comments

10pages. arXiv admin note: substantial text overlap with arXiv:1912.02561

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