Geodesic
Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term
Applications of Mathematics, Tome 68 (2023) no. 2, pp. 209-254 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 conditions to obtain the global solution, we prove the general decay property with positive initial energy for this global solution.\looseness -1
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 conditions to obtain the global solution, we prove the general decay property with positive initial energy for this global solution.\looseness -1
DOI : 10.21136/AM.2022.0200-21
Classification : 35L20, 35L70
Keywords: viscoelastic equations; strong damping; nonlinear memory; general decay 
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     title = {Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term},
     journal = {Applications of Mathematics},
     pages = {209--254},
     year = {2023},
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     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2022.0200-21/}
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Quynh, Doan Thi Nhu; Nhan, Nguyen Huu; Ngoc, Le Thi Phuong; Long, Nguyen Thanh. Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term. Applications of Mathematics, Tome 68 (2023) no. 2, pp. 209-254. doi: 10.21136/AM.2022.0200-21

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