In this paper we investigate a nonlinear viscoelastic equation with nonlinear damping. Global existence of weak solutions and uniform decay of the energy have been established. The Faedo-Galerkin method and the perturbed energy method are employed to obtain the results.

In this paper, we establish the existence and uniqueness of a BV solution to an initial boundary value problem for a nonlinear integro-differential equation, which is related to a denoising and deblurring variational model in image restoration. Several experiments relevant to the restoration model are performed and numerical results are discussed.

In this paper, we have used the homotopy perturbation and the Adomian decomposition methods to study the nonlinear coupled Kortewge-de Vries and shallow water equations. The main objective of this paper is to propose alternative methods of solutions, which do not require small parameters and avoid linearization and physical unrealistic assumptions. The proposed methods give more general exact solutions without much extra effort and the results reveal that the homotopy perturbation and the Adomian decomposition methods are very effective, convenient and quite accurate to the systems of coupled nonlinear equations.

In this paper, we reprove a theorem of M. Anderson [Invent. Math., 69 (1982), pp. 477-494] which established the existence of a minimal hypersurface in the hyperbolic space with prescribed asymptotic boundary with non-negative mean curvature in the non-parametric case. We use the mean curvature flow method.

The aim of this paper is to prove that compressible combustion flow in two and three space dimensions converges to the incompressible flow in the limit as the Mach number tends to zero.

In this paper we establish the existence, uniqueness and long-time behavior of weak solutions for the initial-boundary value problem of a fourth-order degenerate parabolic equation with variable exponent of nonlinearity.