On a nonlinear wave equation with damping.
L. A. Medeiros, M. Milla Miranda (1990)
Revista Matemática de la Universidad Complutense de Madrid
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L. A. Medeiros, M. Milla Miranda (1990)
Revista Matemática de la Universidad Complutense de Madrid
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Mohammed Aassila (1999)
Colloquium Mathematicae
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Wu, Shun-Tang, Tsai, Long-Yi (2006)
Applied Mathematics E-Notes [electronic only]
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Yoshihiro Shibata (1993)
Commentationes Mathematicae Universitatis Carolinae
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The global in time solvability of the one-dimensional nonlinear equations of thermoelasticity, equations of viscoelasticity and nonlinear wave equations in several space dimensions with some boundary dissipation is discussed. The blow up of the solutions which might be possible even for small data is excluded by allowing for a certain dissipative mechanism.
Eduard Feireisl (1990)
Commentationes Mathematicae Universitatis Carolinae
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Irena Lasiecka, Roberto Triggiani (2008)
Control and Cybernetics
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Zhuan Ye (2015)
Colloquium Mathematicae
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We prove the existence and uniqueness of global strong solutions to the Cauchy problem for 3D incompressible MHD equations with nonlinear damping terms. Moreover, the preliminary L² decay for weak solutions is also established.