Displaying similar documents to “A THeorem of Global Existence of Solutions to Nonlinear Wave Equations in Four Space Dimensions.”

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 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.