Quasilinear Wave Equations with Decaying Time-Potential

Vladimir Georgiev*, Sandra Lucente

*この研究の対応する著者

研究成果: Chapter

抄録

An active area of recent research is the study of global existence and blow up for nonlinear wave equations where time depending mass or damping are involved. The interaction between linear and nonlinear terms is a crucial point in determination of global evolution dynamics. When the nonlinear term depends on the derivatives of the solution, the situation is even more delicate. Indeed, even in the constant coefficients case, the null conditions strongly relate the symbol of the linear operator with the form of admissible nonlinear terms which leads to global existence. Some peculiar operators with time-dependent coefficients lead to a wave operator in which the time derivative becomes a covariant time derivative. In this paper we give a blow up result for a class of quasilinear wave equations in which the nonlinear term is a combination of powers of first and second order time derivatives and a time-dependent factor. Then we apply this result to scale invariant damped wave equations with nonlinearity involving the covariant time derivatives.

本文言語English
ホスト出版物のタイトルSpringer INdAM Series
出版社Springer-Verlag Italia s.r.l.
ページ187-204
ページ数18
DOI
出版ステータスPublished - 2022

出版物シリーズ

名前Springer INdAM Series
52
ISSN(印刷版)2281-518X
ISSN(電子版)2281-5198

ASJC Scopus subject areas

  • 数学一般

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