Asymptotic Behavior of Solutions of Quasilinear Hyperbolic Equations with Linear Damping

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 ...

Asymptotic Behavior of Solutions to Half-Linear q-Difference Equations

and Applied Analysis 3 Next we present auxiliary statements which play important roles in proving the main results. Define F : 0,∞ → R by F x Φ x/q−1/q −Φ 1−1/x and h : Φ −∞ q ,∞ → R by h x x 1 − q1−α [ 1 − ( 1 ( q − 1 ) Φ−1 x )1−α] . 2.1 For y : q0 → R \ {0} define the operator L by L [ y ] t Φ ( y ( q2t ) qy ( qt ) − 1 q ) −Φ ( 1 − y t

Asymptotic Behavior of Positive Solutions of Some Quasilinear Elliptic Problems

We discuss the asymptotic behavior of positive solutions of the quasilinear elliptic problem −∆pu = au p−1 − b(x)u, u|∂Ω = 0 as q → p − 1 + 0 and as q → ∞ via a scale argument. Here ∆p is the p-Laplacian with 1 < p < ∞ and q > p−1. If p = 2, such problems arise in population dynamics. Our main results generalize the results for p = 2, but some technical difficulties arising from the nonlinear d...