Quasilinear Wave Equations with Decaying Time-Potential

Vladimir Georgiev*, Sandra Lucente

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

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.

Original languageEnglish
Title of host publicationSpringer INdAM Series
PublisherSpringer-Verlag Italia s.r.l.
Pages187-204
Number of pages18
DOIs
Publication statusPublished - 2022

Publication series

NameSpringer INdAM Series
Volume52
ISSN (Print)2281-518X
ISSN (Electronic)2281-5198

ASJC Scopus subject areas

  • Mathematics(all)

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