In this paper, we shall be concerned with the existence result of the Degenerated unilateral problem associated to the equation of the type where is a Leray-Lions operator and is a Carathéodory function having natural growth with respect to and satisfying the sign condition. The second term is such that, and .
The paper is dedicated to the existence of local solutions of strongly nonlinear equations in RN and the Orlicz spaces framework is used.
We prove the existence of solutions to a differential-functional system which describes a wide class of multi-component populations dependent on their past time and state densities and on their total size. Using two different types of the Hale operator, we incorporate in this model classical von Foerster-type equations as well as delays (past time dependence) and integrals (e.g. influence of a group of species).
This paper has two objectives. First, we prove the existence of solutions to the general advection-diffusion equation subject to a reasonably smooth initial condition. We investigate the behavior of the solution of these problems for large values of time. Secondly, a numerical scheme using the Sinc-Galerkin method is developed to approximate the solution of a simple model of turbulence, which is a special case of the advection-diffusion equation, known as Burgers' equation. The approximate solution...
We examine the Poisson equation with boundary conditions on a cylinder in a weighted space of , p≥ 3, type. The weight is a positive power of the distance from a distinguished plane. To prove the existence of solutions we use our result on existence in a weighted L₂ space.