Article
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Higher Order Wave Equation with Logarithmic Source Term
Version 1
: Received: 26 December 2017 / Approved: 30 December 2017 / Online: 30 December 2017 (14:58:51 CET)
How to cite: Hajrulla, S.; Bezati, L.; Hoxha, F. Higher Order Wave Equation with Logarithmic Source Term. Preprints 2017, 2017120202. https://doi.org/10.20944/preprints201712.0202.v1 Hajrulla, S.; Bezati, L.; Hoxha, F. Higher Order Wave Equation with Logarithmic Source Term. Preprints 2017, 2017120202. https://doi.org/10.20944/preprints201712.0202.v1
Abstract
In this paper we study the initial boundary value problem for logarithmic Higher Order Wave equation. Introducing the Logarithmic Sobolev inequality and using the combination of Galerkin method, we consider the theorem of existence of a global weak solution to problem for the initial boundary value problem of the logarithmic wave equation. By constructing an appropriate Lyapunov function, we obtain the decay estimates of energy for logarithmic Higher Order Wave equation. The proof of the main theorem is given.
Keywords
global existence; damping; boundary source; logarithmic wave equation; initial boundary value problem; decay estimate
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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