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Semi‐linear wave models with power non‐linearity and scale‐invariant time‐dependent mass and dissipation, II
Author(s) -
Palmieri Alessandro,
Reissig Michael
Publication year - 2018
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.201700144
Subject(s) - dissipation , mathematics , linearity , invariant (physics) , mathematical analysis , scale (ratio) , lti system theory , linear system , physics , mathematical physics , quantum mechanics , thermodynamics
This paper is a continuation of our recent paper [8][W. Nunes do Nascimento, 2016]. 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 global existence (in time) of small data energy solutions assuming suitable regularity on the L 2 scale with additional L 1 regularity for the data. In order to deal with this L 2 regularity in the non‐linear part, we will develop and employ some tools from Harmonic Analysis.