Author:
Milla Miranda Manuel,Medeiros Luiz A.,Louredo Aldo T.
Abstract
This article concerns the existence and decay of solutions of a mixed problem for a quasilinear hyperbolic equation which has its motivation in a mathematical model that describes the nonlinear vibrations of the cross-section of a bar.
For more information see https://ejde.math.txstate.edu/Volumes/2020/100/abstr.html
Reference19 articles.
1. H. Brezis; Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, New York, 2011.
2. J. C. Clements; On the existence and uniqueness of solutions of the equation utt− ∂ ∂xi σ(uxi)−∆N ut = f, Canad. Math. Bull., 16(2) (1975), 181-187.
3. M. Dafermos; The mixed initial boundary value problem for equation of nonlinear one dimensional viscoelasticity, J. Differ. Eq., 6(1) (1969), 71-86.
4. G. Giorgi, G. Matarazzo; An existence theorem for nonlinear evolution equation in viscoelasticity, Ann. Univ. Ferrara- Sez. VII- Sc. Mat., XXVI (1980), 113-124.
5. J. M. Greenberg, R. C. MacCamy, V. L. Mizel; On the existence uniqueness and stability of solutions of the equation σ 0(ux)uxxx + λuxtx = ρ0utt, J. Math. and Mech., 17 (1968), 707-728.