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- Publisher
- Springer Journals
- Copyright
- Copyright © 2017 by Springer Science+Business Media New York
- Subject
- Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
- ISSN
- 0095-4616
- eISSN
- 1432-0606
- DOI
- 10.1007/s00245-017-9423-3
- Publisher site
- See Article on Publisher Site
Abstract
We consider the initial boundary value problem for a class of logarithmic wave equations with linear damping. By constructing a potential well and using the logarithmic Sobolev inequality, we prove that, if the solution lies in the unstable set or the initial energy is negative, the solution will grow as an exponential function in the $$H^1_0(\Omega )$$ H 0 1 ( Ω ) norm as time goes to infinity. If the solution lies in a smaller set compared with the stable set, we can estimate the decay rate of the energy. These results are extensions of earlier results.
Journal
Applied Mathematics and Optimization – Springer Journals
Published: Jun 7, 2017