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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Doan Thi Nhu Quynh, Nguyen Huu Nhan, Le Thi Phuong Ngoc, Nguyen Thanh Long (2023)
Applications of Mathematics
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We study existence, uniqueness, continuous dependence, general decay of solutions of an initial boundary value problem for a viscoelastic wave equation with strong damping and nonlinear memory term. At first, we state and prove a theorem involving local existence and uniqueness of a weak solution. Next, we establish a sufficient condition to get an estimate of the continuous dependence of the solution with respect to the kernel function and the nonlinear terms. Finally, under suitable...
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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