Global Existence and General Decay of Solutions for a Quasilinear System with Degenerate Damping Terms
نویسندگان
چکیده
In this work, we consider a quasilinear system of viscoelastic equations with degenerate damping, dispersion, and source terms under Dirichlet boundary condition. Under some restrictions on the initial datum standard conditions relaxation functions, study global existence general decay solutions. The results obtained here are generalization previous recent work.
منابع مشابه
Global existence, decay and blow up solutions for coupled nonlinear wave equations with damping and source terms
We study the initial-boundary value problem for a system of nonlinear wave equations with nonlinear damping and source terms, in a bounded domain. The decay estimates of the energy function are established by using Nakao’s inequality. The nonexistence of global solutions is discussed under some conditions on the given parameters.
متن کاملExistence of at least three weak solutions for a quasilinear elliptic system
In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...
متن کاملExistence of solutions for quasilinear degenerate elliptic equations ∗
In this paper, we study the existence of solutions for quasilinear degenerate elliptic equations of the form A(u) + g(x, u,∇u) = h, where A is a Leray-Lions operator from W 1,p 0 (Ω, w) to its dual. On the nonlinear term g(x, s, ξ), we assume growth conditions on ξ, not on s, and a sign condition on s.
متن کاملOn the decay of solutions for a class of quasilinear hyperbolic equations with non-linear damping and source terms
In this paper, we consider the non-linear wave equation utt − ut − div(|∇u|∇u) + a|ut | ut = b|u|u a; b¿0, associated with initial and Dirichlet boundary conditions. Under suitable conditions on , m, and p, we give precise decay rates for the solution. In particular, we show that for m = 0, the decay is exponential. This work improves the result by Yang (Math. Meth. Appl. Sci. 2002; 25:795–814)...
متن کاملOptimal decay rates and global existence for a semilinear Timoshenko system with two damping effects
In this paper, we study a semilinear Timoshenko system having two damping effects. The observation that two damping effects might lead to smaller decay rates for solutions in comparison to one damping effect is rigorously proved here in providing optimality results. Moreover the global well-posedness for small data in a low regularity class is presented for a larger class of nonlinearities than...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of function spaces
سال: 2021
ISSN: ['2314-8896', '2314-8888']
DOI: https://doi.org/10.1155/2021/4316238