Results 21 to 30 of about 717 (67)

Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces

Open Mathematics, 2016
We obtain the global weighted Morrey-type regularity of the solution of the regular oblique derivative problem for linear uniformly parabolic operators with VMO coefficients.
Guliyev Vagif S., Omarova Mehriban N.
doaj   +1 more source

Two-phase heat conductors with a stationary isothermic surface [PDF]

, 2016
We consider a two-phase heat conductor in $\mathbb R^N$ with $N \geq 2$ consisting of a core and a shell with different constant conductivities.
Sakaguchi, Shigeru
core   +3 more sources

On the weak solution of a three‐point boundary value problem for a class of parabolic equations with energy specification

Abstract and Applied Analysis, Volume 2003, Issue 10, Page 573-589, 2003., 2003
This paper deals with weak solution in weighted Sobolev spaces, of three‐point boundary value problems which combine Dirichlet and integral conditions, for linear and quasilinear parabolic equations in a domain with curved lateral boundaries. We, firstly, prove the existence, uniqueness, and continuous dependence of the solution for the linear equation.
Abdelfatah Bouziani
wiley   +1 more source

Rothe method for a mixed problem with an integral condition for the two‐dimensional diffusion equation

Abstract and Applied Analysis, Volume 2003, Issue 16, Page 899-922, 2003., 2003
This paper deals with an initial boundary value problem with an integral condition for the two‐dimensional diffusion equation. Thanks to an appropriate transformation, the study of the given problem is reduced to that of a one‐dimensional problem. Existence, uniqueness, and continuous dependence upon data of a weak solution of this latter are proved by
Nabil Merazga, Abdelfatah Bouziani
wiley   +1 more source

Time‐dependent Stokes equations with measure data

Abstract and Applied Analysis, Volume 2003, Issue 17, Page 953-973, 2003., 2003
We establish the existence of a unique solution of an initial boundary value problem for the nonstationary Stokes equations in a bounded fixed cylindrical domain with measure data. Feedback laws yield the source and its intensity from the partial measurements of the solution in a subdomain.
Bui An Ton
wiley   +1 more source

On the existence of positive solutions for periodic parabolic sublinear problems

Abstract and Applied Analysis, Volume 2003, Issue 17, Page 975-984, 2003., 2003
We give necessary and sufficient conditions for the existence of positive solutions for sublinear Dirichlet periodic parabolic problems Lu = g(x, t, u) in Ω × ℝ (where Ω ⊂ ℝN is a smooth bounded domain) for a wide class of Carathéodory functions g : Ω × ℝ × [0, ∞) → ℝ satisfying some integrability and positivity conditions.
T. Godoy, U. Kaufmann
wiley   +1 more source

Variational analysis for simulating free‐surface flows in a porous medium

Journal of Applied Mathematics, Volume 2003, Issue 8, Page 377-396, 2003., 2003
A variational formulation has been developed to solve a parabolic partial differential equation describing free‐surface flows in a porous medium. The variational finite element method is used to obtain a discrete form of equations for a two‐dimensional domain.
Shabbir Ahmed, Charles Collins
wiley   +1 more source

UNIFORM BMO ESTIMATE OF PARABOLIC EQUATIONS AND GLOBAL WELL-POSEDNESS OF THE THERMISTOR PROBLEM

Forum of Mathematics, Sigma, 2015
We prove global well-posedness of the time-dependent degenerate thermistor problem by establishing a uniform-in-time bounded mean ocsillation (BMO) estimate of inhomogeneous parabolic equations.
BUYANG LI, CHAOXIA YANG
doaj   +1 more source

A PDAE formulation of parabolic problems with dynamic boundary conditions

, 2018
The weak formulation of parabolic problems with dynamic boundary conditions is rewritten in form of a partial differential-algebraic equation. More precisely, we consider two dynamic equations with a coupling condition on the boundary. This constraint is
Altmann, Robert
core   +1 more source

On the solvability of a class of singular parabolic equations with nonlocal boundary conditions in nonclassical function spaces

International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 7, Page 435-447, 2002., 2002
The aim of this paper is to prove the existence, uniqueness, and continuous dependence upon the data of a generalized solution for certain singular parabolic equations with initial and nonlocal boundary conditions. The proof is based on an a priori estimate established in nonclassical function spaces, and on the density of the range of the operator ...
Abdelfatah Bouziani
wiley   +1 more source