Global existence for nonlinear system of wave equations in 3-D domains

Jianwei Yang

Displaying similar documents to “Global existence for nonlinear system of wave equations in 3-D domains”

Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term

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...

On a global in time existence theorem of smooth solutions to an nonlinear wave equation with viscosity.

T. Koboyashi, H. Pecher, Y. Shibata (1993)

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Global in time solvability of the initial boundary value problem for some nonlinear dissipative evolution equations

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.

Regularization and finite element approximation of the wave equation with Dirichlet boundary data

I. Lasiecka, J. Sokołowski, P. Neittaanmäki (1990)

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Strichartz estimates for the wave equation on manifolds with boundary

Matthew D. Blair, Hart F. Smith, Christopher D. Sogge (2009)

Annales de l'I.H.P. Analyse non linéaire

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Remarks on the existence an uniqueness of global decaying solutions of the nonlinear dissipative wave equations.

Mitsuhiro Nakao (1991)

Mathematische Zeitschrift

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On the Decay of Solutions of Some Nonlinear Dissipative Wave Equations in Higher Dimensions.

Mitsuhiro Nakao (1986)

Mathematische Zeitschrift

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Initial value problems in elasticity

Rolf Leis (1992)

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Blowup of solutions of a nonlinear wave equation.

Benaissa, Abbes, Messaoudi, Salim A. (2002)

Journal of Applied Mathematics

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Weak solutions to the initial boundary value problem for a semilinear wave equation with damping and source terms

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...

On the nonlinear stabilization of the wave equation

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.