Long-time behavior of nonlinear elastic waves
Thomas C. Sideris (1995)
Journées équations aux dérivées partielles
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Thomas C. Sideris (1995)
Journées équations aux dérivées partielles
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Rolf Leis (1992)
Banach Center Publications
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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...
P. Donnat, J.-L. Joly, G. Métivier, J. Rauch (1995-1996)
Séminaire Équations aux dérivées partielles (Polytechnique)
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Viorel Barbu, Irena Lasiecka, Mohammad Rammaha (2005)
Control and Cybernetics
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Christopher D. Sogge (1993)
Journées équations aux dérivées partielles
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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.
Igor Rodnianski (2005-2006)
Séminaire Bourbaki
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The paper provides a description of the wave map problem with a specific focus on the breakthrough work of T. Tao which showed that a wave map, a dynamic lorentzian analog of a harmonic map, from Minkowski space into a sphere with smooth initial data and a small critical Sobolev norm exists globally in time and remains smooth. When the dimension of the base Minkowski space is , the critical norm coincides with energy, the only manifestly conserved quantity in this (lagrangian) theory....
Sergiù Klainerman, Damiano Foschi (1999)
Journées équations aux dérivées partielles
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I will start with a short review of the classical restriction theorem for the sphere and Strichartz estimates for the wave equation. I then plan to give a detailed presentation of their recent generalizations in the form of “Bilinear Estimates”. In addition to the theory, which is now quite well developed, I plan to discuss a more general point of view concerning the theory. By investigating simple examples I will derive necessary conditions for such estimates to be true. I also...