On a wave equation with singular dissipation
Mohammed ElAmine Sebih, Jens Wirth
TL;DR
This paper investigates a wave equation with highly singular dissipation terms, developing phase-space analysis tools to understand how solutions' singularities interact with the equation's strong singular coefficients.
Contribution
It introduces new analytical methods for phase-space analysis of wave equations with distributional and more singular coefficients, focusing on singularity interactions.
Findings
Detailed analysis of singularity interactions in the wave equation
Development of tools for phase-space analysis of singular PDEs
Insights into the behavior of solutions with singular coefficients
Abstract
In this paper we consider a singular wave equation with distributional and more singular non-distributional coefficients and develop tools and techniques for the phase-space analysis of such problems. In particular we provide a detailed analysis for the interaction of singularities of solutions with strong singularities of the coefficient in a model problem of recent interest.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Stability and Controllability of Differential Equations · Differential Equations and Boundary Problems