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11-01-2020 | Focus

Global well-posedness for the nonlinear damped wave equation with logarithmic type nonlinearity

Authors: Lu Yang, Wei Gao

Published in: Soft Computing | Issue 4/2020

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Abstract

The initial boundary value problem for the nonlinear wave equations with damping and logarithmic nonlinearity is investigated in this paper. By making use of modified potential well theory and the technique of Logarithmic-Sobolev inequality, we establish global existence as well as asymptotic behavior of solution, under the assumption that the initial energy is small. Moreover, we obtain an exponential decay which is much faster than the decay in polynomial nonlinear case of Gazzola and Squassina (Ann I H Poincaré AN 23:185–207, 2006). These results generalize and extend work in application of potential well theory to wave equations.

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Title: Global well-posedness for the nonlinear damped wave equation with logarithmic type nonlinearity
Authors: Lu Yang
Wei Gao
Publication date: 11-01-2020
Publisher: Springer Berlin Heidelberg
Published in: Soft Computing / Issue 4/2020
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-019-04660-6

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