We consider a system of semilinear partial differential equations (PDEs) with nonlinearity depending on both the solution and its gradient. The Neumann boundary condition depends in nonlinear manner. uniform ellipticity is not required for diffusion coefficient. show that this problem admits viscosity which can be approximated by penalization. Lipschitz coefficients part. part as well are Lipsc...

The theory of time scales was introduced by Hilger in his Ph.D. thesis 1 in 1988 in order to unify continuous and discrete analysis. The study of dynamic equations on time scales is a fairly new subject and research in this area is rapidly growing. For some basic definitions and relevant results on time scales, see 2, 3 . Recently, first-order boundary value problems BVPs for short on time scal...

Abstract. The Benjamin-Feir instability describes the instability of a uniform oscillatory wave train in an irrotational flow subject to small perturbation of wave number, amplitude and frequency. Their instability analysis is based on the perturbation around the second order Stokes wave which satisfies the dynamic and kinematic free-surface boundary conditions up to the second order. In the sa...

We discuss the behaviour of a model of ferroelectric material represented by a thin cylinder with small thickness ν > 0. This model is described by a couple of Maxwell equations satisfied by the electromagnetic field (H,E) and electric polarization field P . We give a complete description of the limit model as ν → 0 in the linear case when (E,H) and P satisfy a SilverMüller type boundary condit...

A nonlinear degenerate convection-diffusion initial boundary value problem is studied in a bounded domain. A dynamical boundary condition (containing the time derivative of a solution) is prescribed on the one part of the boundary. This models a non-perfect contact on the boundary. Existence and uniqueness of a weak solution in corresponding function spaces is proved using the backward Euler me...

The existence of infinitely many solutions is established for a class of nonlinear functionals involving the p-biharmonic operator with nonhomoge- neous Neumann boundary conditions. Using a recent critical-point theorem for nonsmooth functionals and under appropriate behavior of the nonlinear term and nonhomogeneous Neumann boundary conditions, we obtain the result.