Focusing NLKG equation with singular potential

Vladimir Georgiev, Sandra Lucente

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We study the dynamics for the focusing nonlinear Klein Gordon equation with a positive, singular, radial potential and initial data in energy space. More precisely, we deal with utt - Δu + m2u = |x|-a|u|p-1u with 0 < a < 2. In dimension d ≥ 3, we establish the existence and uniqueness of the ground state solution that enables us to define a threshold size for the initial data that separates global existence and blow-up. We find a critical exponent depending on a. We establish a global existence result for subcritical exponents and subcritical energy data. For subcritical exponents and critical energy some solutions blow-up, other solutions exist for all time due to the decomposition of the energy space of the initial data into two complementary sets.

Original languageEnglish
Pages (from-to)1387-1406
Number of pages20
JournalCommunications on Pure and Applied Analysis
Volume17
Issue number4
DOIs
Publication statusPublished - 2018 Jul

Keywords

  • Blow up
  • Critical energy
  • Global existence
  • Ground state

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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