On Global Solvability of Nonlinear Kirchhoff Model in Infinitely Increasing Moving Domains |
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Authors: | Rachid Benabidallah FranÇois Ebobisse |
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Institution: | 1. Dipartimento di Matematica , Università di Torino , Via C. Alberto 10, Torino, 10123, Italy;2. SISSA / ISAS , Via Beirut 2-4, Trieste, 34014, Italy |
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Abstract: | The purpose of this article is to study the existence and uniqueness of global solution for the nonlinear hyperbolic-parabolic equation of Kirchhoff-Carrier type: $$ u_{tt} + \mu u_t - M\left (\int _{\Omega _t}|\nabla u|^2dx\right )\Delta u = 0\quad \hbox {in}\ \Omega _t\quad \hbox {and}\quad u|_{\Gamma _t} = \dot \gamma $$ where $ \Omega _t = \{x\in {\shadR}^2 | \ x = y\gamma (t), \ y\in \Omega \} $ with boundary o t , w is a positive constant and n ( t ) is a positive function such that lim t M X n ( t ) = + X . The real function M is such that $ M(r) \geq m_0 \gt 0 \forall r\in 0,\infty $ . |
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Keywords: | Nonlinear Hyperbolic-parabolic Equation Kirchhoff Model Moving Domain Global Solution |
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