Critical regularity of nonlinearities in semilinear classical damped wave equations
Reissig, Michael
2020Università Politecnica delle Marche (Università Politecnica delle Marche)33 citationsDOIOpen Access PDF
Abstract
In this paper we consider the Cauchy problem for the semilinear damped wave equation utt-Δu+ut=h(u),u(0,x)=φ(x),ut(0,x)=ψ(x),where h(s)=|s|1+2nμ(|s|). Here n is the space dimension and μ is a modulus of continuity. Our goal is to obtain sharp conditions on μ to obtain a threshold between global (in time) existence of small data solutions (stability of the zero solution) and blow-up behavior even of small data solutions
Topics & Concepts
MathematicsDimension (graph theory)Wave equationMathematical analysisSpace (punctuation)Zero (linguistics)Damped waveInitial value problemStability (learning theory)Mathematical physicsCauchy distributionPure mathematicsMachine learningPhilosophyLinguisticsComputer scienceAdvanced Mathematical Physics ProblemsNavier-Stokes equation solutionsStability and Controllability of Differential Equations