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Semi‐linear wave models with power non‐linearity and scale‐invariant time‐dependent mass and dissipation
Author(s) -
Nunes do Nascimento Wanderley,
Palmieri Alessandro,
Reissig Michael
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600069
Subject(s) - dissipation , mathematics , linearity , invariant (physics) , nonlinear system , scale invariance , mathematical analysis , scale (ratio) , lti system theory , control theory (sociology) , statistics , linear system , physics , mathematical physics , computer science , thermodynamics , quantum mechanics , control (management) , artificial intelligence
In this paper we will consider the semi‐linear Cauchy problem for wave models with scale‐invariant time‐dependent mass and dissipation and power non‐linearity. The goal is to study the interplay between the coefficients of the mass and the dissipation term to prove blow‐up results or global existence (in time) of small data energy solutions.