On some nonlinear problem for the thermoplate equations

${author.authorNameEn}; Hirokazu Saito; Yoshihiro Shibata

doi:10.3934/eect.2019037

Article Contents

2019, Volume 8, Issue 4: 755-784. Doi: 10.3934/eect.2019037

This issue Previous Article Discontinuous solutions for the generalized short pulse equation Next Article A new energy-gap cost functional approach for the exterior Bernoulli free boundary problem

On some nonlinear problem for the thermoplate equations

1.
Department of Pure and Applied Mathematics, Graduate School of Waseda Univeristy, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan
2.
Department of Mathematics, Faculty of Science and Technology, Syarif Hiayatullah State Islamic University, Jl. Ir. H. Juanda No. 95, Ciputat Tangerang 15412, Indonesia
3.
Faculty of Industrial Science and Technology, Tokyo University of Science, 102-1 Tomino, Oshamambe-cho, Yamakoshi-gun, Hokkaido 049-3514, Japan
4.
Department of Pure and Applied Mathematics and Research Institute of Science and Engineering, Waseda Univeristy, Ohkubo 3-4-1, Shinjuku-ku, Tokyo 169-8555, Japan
5.
Department of Mechanical Engineering and Material Science, University of Pittsburgh, USA

^* Corresponding author: Suma'inna
^* Corresponding author: Suma'inna

Received: June 30, 2018

Revised: December 31, 2018

Early access: June 2019

Published: June 2019

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Abstract

In this paper, we prove the local and global well-posedness of some nonlinear thermoelastic plate equations with Dirichlet boundary conditions. The main tool for proving the local well-posedness is the maximal $ L_p $-$ L_q $ regularity theorem for the linearized equations, and the main tool for proving the global well-posedness is the exponential stability of $ C_0 $ analytic semigroup associated with linear thermoelastic plate equations with Dirichlet boundary conditions.

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Mathematics Subject Classification: Primary: 35K51, 74F05; Secondary: 93B05.

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