On the Decay of Solutions of Some Nonlinear Dissipative Wave Equations in Higher Dimensions.
Mitsuhiro Nakao (1986)
Mathematische Zeitschrift
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Mitsuhiro Nakao (1986)
Mathematische Zeitschrift
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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...
Petronela Radu (2008)
Applicationes Mathematicae
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We show local existence of solutions to the initial boundary value problem corresponding to a semilinear wave equation with interior damping and source terms. The difficulty in dealing with these two competitive forces comes from the fact that the source term is not a locally Lipschitz function from H¹(Ω) into L²(Ω) as typically assumed in the literature. The strategy behind the proof is based on the physics of the problem, so it does not use the damping present in the equation. The...
Bui Duc Nam, Nguyen Huu Nhan, Le Thi Phuong Ngoc, Nguyen Thanh Long (2022)
Mathematica Bohemica
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We study a system of nonlinear wave equations of the Kirchhoff-Carrier type containing a variant of the Balakrishnan-Taylor damping in nonlinear terms. By the linearization method together with the Faedo-Galerkin method, we prove the local existence and uniqueness of a weak solution. On the other hand, by constructing a suitable Lyapunov functional, a sufficient condition is also established to obtain the exponential decay of weak solutions.
Hartmut Pecher, Robert Glassey (1982)
Manuscripta mathematica
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Papanicolaou, George (1998)
Documenta Mathematica
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Z. Godziński, L. Stasierski (1972)
Applicationes Mathematicae
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Benaissa, Abbes, Messaoudi, Salim A. (2002)
Journal of Applied Mathematics
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Mitsuhiro Nakao (1991)
Mathematische Zeitschrift
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Gera, Dinesh, Gautam, Mridul, Gangarao, Hota V.S. (1997)
International Journal of Mathematics and Mathematical Sciences
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Bhatti, Zahid Rafiq, Durrani, Ijaz-Ur-Rahman (2001)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Bogdan Przeradzki, Katarzyna Szymańska-Dębowska (2014)
Banach Center Publications
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The existence of a traveling wave with special properties to modified KdV and BKdV equations is proved. Nonlinear terms in the equations are defined by means of a function f of an unknown u satisfying some conditions.
Yang Zhifeng (2008)
Open Mathematics
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The initial boundary value problem for a viscoelastic equation with nonlinear damping in a bounded domain is considered. By modifying the method, which is put forward by Li, Tasi and Vitillaro, we sententiously proved that, under certain conditions, any solution blows up in finite time. The estimates of the life-span of solutions are also given. We generalize some earlier results concerning this equation.
Mohammed Aassila (1999)
Commentationes Mathematicae Universitatis Carolinae
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In this note we prove the exponential decay of solutions of a quasilinear wave equation with linear damping and source terms.