6533b7d1fe1ef96bd125d983

RESEARCH PRODUCT

A blow-up result for a nonlinear wave equation on manifolds: the critical case

Mohamed JleliBessem SametCalogero Vetro

subject

manifoldApplied MathematicsBlow-upMathematical analysisBoundary (topology)Riemannian manifoldWave equationManifoldcritical caseDimension (vector space)Settore MAT/05 - Analisi MatematicaNonlinear wave equationMathematics::Differential Geometryinhomogeneous semilinear wave equationAnalysisMathematics

description

We consider a inhomogeneous semilinear wave equation on a noncompact complete Riemannian manifold (Formula presented.) of dimension (Formula presented.), without boundary. The reaction exhibits the combined effects of a critical term and of a forcing term. Using a rescaled test function argument together with appropriate estimates, we show that the equation admits no global solution. Moreover, in the special case when (Formula presented.), our result improves the existing literature. Namely, our main result is valid without assuming that the initial values are compactly supported.

yearjournalcountryeditionlanguage
2021-10-01Applicable Analysis
https://doi.org/10.1080/00036811.2021.1986026