Focusing NLKG equation with singular potential

Vladimir Georgiev*, Sandra Lucente

*この研究の対応する著者

研究成果: Article査読

2 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)1387-1406
ページ数20
ジャーナルCommunications on Pure and Applied Analysis
17
4
DOI
出版ステータスPublished - 2018 7月

ASJC Scopus subject areas

  • 分析
  • 応用数学

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