English

Short time blow-up by negative mass term for semilinear wave equations with small data and scattering damping

Analysis of PDEs 2021-01-19 v1

Abstract

In this paper we study blow-up and lifespan estimate for solutions to the Cauchy problem with small data for semilinear wave equations with scattering damping and negative mass term. We show that the negative mass term will play a dominant role when the decay of its coefficients is not so fast, thus the solutions will blow up in a finite time. What is more, we establish a lifespan estimate from above which is much shorter than the usual one.

Keywords

Cite

@article{arxiv.1905.08100,
  title  = {Short time blow-up by negative mass term for semilinear wave equations with small data and scattering damping},
  author = {Ning-An Lai and Nico Michele Schiavone and Hiroyuki Takamura},
  journal= {arXiv preprint arXiv:1905.08100},
  year   = {2021}
}

Comments

14 pages. Accepted by a guest editor of a special volume on MSJ-SI 2018 in the journal of Advanced Studies in Pure Mathematics