Existence of solutions of the Darboux problem for partial differential equations in Banach spaces
Existence of solutions to a phase-field model with phase-dependent heat absorption.
Existence of solutions to a second order partial differential equation with nonlocal conditions.
Existence of solutions to a superlinear -Laplacian equation.
Existence of solutions to generalized von Foerster equations with functional dependence
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).
Existence of solutions to indefinite quasilinear elliptic problems of --Laplacian type.
Existence of solutions to microhyperbolic boundary value problems
Existence of solutions to -dimensional pendulum-like equations.
Existence of solutions to nonlinear advection-diffusion equation applied to Burgers' equation using Sinc methods
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...
Existence of solutions to nonlinear parabolic problems with delay.
Existence of solutions to nonlocal and singular elliptic problems via Galerkin method.
Existence of solutions to nonlocal and singular variational elliptic inequality via Galerkin method.
Existence of solutions to -Laplace equations with logarithmic nonlinearity.
Existence of solutions to quasilinear functional differential equations.
Existence of solutions to singular elliptic equations with convection terms via the Galerkin method.
Existence of solutions to the Poisson equation in -weighted spaces
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.
Existence of solutions to the Poisson equation in L₂-weighted spaces
We consider the Poisson equation with the Dirichlet and the Neumann boundary conditions in weighted Sobolev spaces. The weight is a positive power of the distance to a distinguished plane. We prove the existence of solutions in a suitably defined weighted space.
Existence of solutions to the Rosenau and Benjamin-Bona-Mahony equation in domains with moving boundary.
Existence of solutions to the (rot,div)-system in -weighted spaces
The existence of solutions to the elliptic problem rot v = w, div v = 0 in a bounded domain Ω ⊂ ℝ³, , S = ∂Ω in weighted -Sobolev spaces is proved. It is assumed that an axis L crosses Ω and the weight is a negative power function of the distance to the axis. The main part of the proof is devoted to examining solutions of the problem in a neighbourhood of L. The existence in Ω follows from the technique of regularization.