Existence and a general decay result for a plate equation with nonlinear damping and a logarithmic source term

Mohammad M. Al-Gharabli; Salim A. Messaoudi

doi:10.1007/s00028-017-0392-4

Existence and a general decay result for a plate equation with nonlinear damping and a logarithmic source term

Mohammad M. Al-Gharabli^*, Salim A. Messaoudi

^*Corresponding author for this work

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47 Scopus citations

Abstract

In this paper, we consider a plate equation with a logarithmic nonlinearity in the presence of nonlinear frictional damping. Using the Galaerkin method, we establish the existence of solutions of the problem and we prove an explicit and general decay rate result, using the multiplier method and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term.

Original language	English
Pages (from-to)	105-125
Number of pages	21
Journal	Journal of Evolution Equations
Volume	18
Issue number	1
DOIs	https://doi.org/10.1007/s00028-017-0392-4
State	Published - 1 Mar 2018

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Publisher Copyright:
© 2017, Springer International Publishing.

ASJC Scopus subject areas

Mathematics (miscellaneous)

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10.1007/s00028-017-0392-4

Cite this

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title = "Existence and a general decay result for a plate equation with nonlinear damping and a logarithmic source term",

abstract = "In this paper, we consider a plate equation with a logarithmic nonlinearity in the presence of nonlinear frictional damping. Using the Galaerkin method, we establish the existence of solutions of the problem and we prove an explicit and general decay rate result, using the multiplier method and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term.",

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AU - Al-Gharabli, Mohammad M.

AU - Messaoudi, Salim A.

PY - 2018/3/1

Y1 - 2018/3/1

N2 - In this paper, we consider a plate equation with a logarithmic nonlinearity in the presence of nonlinear frictional damping. Using the Galaerkin method, we establish the existence of solutions of the problem and we prove an explicit and general decay rate result, using the multiplier method and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term.

AB - In this paper, we consider a plate equation with a logarithmic nonlinearity in the presence of nonlinear frictional damping. Using the Galaerkin method, we establish the existence of solutions of the problem and we prove an explicit and general decay rate result, using the multiplier method and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term.

UR - https://www.scopus.com/pages/publications/85018455139

U2 - 10.1007/s00028-017-0392-4

DO - 10.1007/s00028-017-0392-4

M3 - Article

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JO - Journal of Evolution Equations

JF - Journal of Evolution Equations

IS - 1

ER -

Existence and a general decay result for a plate equation with nonlinear damping and a logarithmic source term

Abstract

Bibliographical note

ASJC Scopus subject areas

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