Existence and asymptotic behaviour for a degenerate kirchhoff-carrier model with viscosity and nonlinear boundary conditions

Abstract

The present paper studies the existence and uniqueness of global solutions and decay rates to the nonlinear hyperbolic problemwhere M is a C 1 function; M (λ) ≥ 0; ∀λ ≥ 0.

On a Kirchhoff wave model with nonlocal nonlinear damping

“…Later, in Chueshov [4] is considered the strong case θ = 1. More precisely, it is studied in [4] the following Kirchhoff wave model with nonlocal and nonlinear strong damping u tt − φ( ∇u(t) 2 2 )∆u − σ( ∇u(t) 2 2 )∆u t + f (u) = h.…”

“…Introduction. In this paper we address well-posedness and long-time behavior to the following quasi-linear Kirchhoff wave model with nonlocal nonlinear damping u tt − φ( ∇u(t) 2 2 )∆u + σ ∇u(t) 2 2 g(u t ) + f (u) = h in Ω × (0, ∞),…”

“…The main object of study of this paper is to analyze the existence and asymptotic behavior of solutions for (1)- (2) under the influence of the nonlocal nonlinear damping term σ ∇u(t) 2 2 g(u t ).…”

On a Nonlinear Wave Equation of Kirchhoff-Carrier Type: Linear Approximation and Asymptotic Expansion of Solution in a Small Parameter

“…Cavalcanti et al, in [4][5][6][7], investigated a series of four papers in which the results of existence, global existence, exponential or uniform decay rates, and asymptotic behavior for Kirchhoff-Carrier models are considered.…”

“…Therefore, it is clear that (1) considered here contains (4) and (5) as special cases. Moreover, with various boundary conditions, the particular forms of (1) have been extensively studied by many authors; for example, we refer to [3][4][5][6][7][8][9][10][11][12][13][14][15] and the references given therein. In these works, many interesting results about existence, regularity, asymptotic behavior, asymptotic expansion, and decay of solutions were obtained.…”