On the Wave Equation with Space Dependent Coefficients: Singularities and Lower Order Terms
Copyright policy )On the Wave Equation with Space Dependent Coefficients: Singularities and Lower Order Terms
AbstractThis paper complements the study of the wave equation with discontinuous coefficients initiated in (Discacciati et al. in J. Differ. Equ.319 (2022) 131–185) in the case of time-dependent coefficients. Here we assume that the equation coefficients are depending on space only and we formulate Levi conditions on the lower order terms to guarantee the existence of a very weak solution as defined in (Garetto and Ruzhansky in Arch. Ration. Mech. Anal.217 (2015) 113–154). As a toy model we study the wave equation in conservative form with discontinuous velocity and we provide a qualitative analysis of the corresponding very weak solution via numerical methods.
- Queen Mary University of London United Kingdom
- Department of Mathematical Sciences Loughborough University United Kingdom
- Queen Mary University of London
- Loughborough University United Kingdom
- White Rose Consortium: University of Leeds; University of Sheffield; University of York United Kingdom
PDEs with low regular coefficients and/or low regular data, Hyperbolic equations, very weak solutions, Generalized solutions to partial differential equations, Initial value problems for second-order hyperbolic equations, Regularisation, hyperbolic equations, Mathematics - Analysis of PDEs, 35L05, 35L10, 35D99, regularisation, FOS: Mathematics, Very weak solutions, Analysis of PDEs (math.AP)
PDEs with low regular coefficients and/or low regular data, Hyperbolic equations, very weak solutions, Generalized solutions to partial differential equations, Initial value problems for second-order hyperbolic equations, Regularisation, hyperbolic equations, Mathematics - Analysis of PDEs, 35L05, 35L10, 35D99, regularisation, FOS: Mathematics, Very weak solutions, Analysis of PDEs (math.AP)
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).3 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!