Global existence and energy decay rates for a Kirchhoff-type wave equation with nonlinear dissipation

Daewook Kim; Dojin Kim; Keum Shik Hong; Il Hyo Jung

doi:10.1155/2014/716740

Global existence and energy decay rates for a Kirchhoff-type wave equation with nonlinear dissipation

Daewook Kim, Dojin Kim, Keum Shik Hong, Il Hyo Jung

Department of Mathematics

Pusan National University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form Ku′′+MA1/2u2Au+gu′=0 under suitable assumptions on K,A,M(·), and g(·). Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipation g. Lastly, numerical simulations in order to verify the analytical results are given.

Original language	English
Article number	716740
Journal	Scientific World Journal
Volume	2014
DOIs	https://doi.org/10.1155/2014/716740
State	Published - 2014

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title = "Global existence and energy decay rates for a Kirchhoff-type wave equation with nonlinear dissipation",

abstract = "The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form Ku′′+MA1/2u2Au+gu′=0 under suitable assumptions on K,A,M(·), and g(·). Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipation g. Lastly, numerical simulations in order to verify the analytical results are given.",

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N2 - The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form Ku′′+MA1/2u2Au+gu′=0 under suitable assumptions on K,A,M(·), and g(·). Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipation g. Lastly, numerical simulations in order to verify the analytical results are given.

AB - The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form Ku′′+MA1/2u2Au+gu′=0 under suitable assumptions on K,A,M(·), and g(·). Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipation g. Lastly, numerical simulations in order to verify the analytical results are given.

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Global existence and energy decay rates for a Kirchhoff-type wave equation with nonlinear dissipation

Abstract

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