Preprint Article Version 1 This version is not peer-reviewed

# 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 (doi: 10.20944/preprints201712.0202.v1). Hajrulla, S.; Bezati, L.; Hoxha, F. Higher Order Wave Equation with Logarithmic Source Term. Preprints 2017, 2017120202 (doi: 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.

## Subject Areas

global existence; damping; boundary source; logarithmic wave equation; initial boundary value problem; decay estimate

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