Asymptotic Behaviors of Solutions of Quasilinear Hyperbolic Equations with Linear Damping II

Asymptotic Behavior of Solutions to Quasilinear Hyperbolic Equations with Nonlinear Damping

On 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)...

Asymptotic Behavior of the Solutions of Linear and Quasilinear Elliptic Equations on R

We investigate the relationship between the decay at infinity of the right-hand side f and solutions u of an equation Lu = f when L is a second order elliptic operator on RN . It is shown that when L is Fredholm, u inherits the type of decay of f (for instance, exponential, or power-like). In particular, the generalized eigenfunctions associated with all the Fredholm eigenvalues of L, isolated ...

Existence and Uniqueness of Solutions of Quasilinear Wave Equations (ii)

In this work we prove a result concernig the existence and uniqueness of solutions of quasilinear wave equation and we consider also their trivial solutions. We consider the following initial-boundary value problem for the nonlinear wave equation in the form u+ f (u) + g (u̇) = 0 in [0, T ) × Ω (QL) with initial values u0 = u (0, ·) , u1 = u̇ (0, ·) and boundary vale null, that is, u (t, x) = 0 o...

Solutions of Semilinear Elliptic Equations with Asymptotic Linear Nonlinearity

In this paper, we consider some semilinear elliptic equations with asymptotic linear nonlinearity and show the existence, uniqueness, and asymptotic behavior of these solutions.