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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Robert T. Glassey (1973)
Mathematische Zeitschrift
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Aissa Guesmia (1998)
Annales Polonici Mathematici
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We obtain a precise decay estimate of the energy of the solutions to the initial boundary value problem for the wave equation with nonlinear internal and boundary feedbacks. We show that a judicious choice of the feedbacks leads to fast energy decay.
Robert T. Glassey (1981)
Mathematische Zeitschrift
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Mitsuhiro Nakao (1991)
Mathematische Zeitschrift
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Hiroyuki Takamura (1994)
Mathematische Zeitschrift
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Mitsuhiro Nakao (1996)
Mathematische Annalen
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Peter Kumlin (1988)
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Felix E. Browder (1962/63)
Mathematische Zeitschrift
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Jean-Claude Guillot, Calvin H. Wilcox (1978)
Mathematische Zeitschrift
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Tohru Ozawa (1991)
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...
Wolf von Wahl (1975)
Mathematische Zeitschrift
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Kovriguine, D.A., Maugin, G.A., Potapov, A.I. (2006)
Mathematical Problems in Engineering
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