Results 31 to 40 of about 804 (84)

Asymptotic stability for a symmetric parabolic problem modeling Ohmic heating

Boundary Value Problems, 2014
We consider the asymptotic behavior of the solution of the non-local parabolic equation ut=(κ(u))rr+(κ(u))rr+f(u)(a+2πb∫01f(u)rdr)2, for 00, with a homogeneous Dirichlet boundary condition.
Mingshu Fan, Anyin Xia, Lei Zhang
semanticscholar   +2 more sources

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

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

On the solvability of parabolic and hyperbolic problems with a boundary integral condition

International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 4, Page 201-213, 2002., 2002
We prove the existence, uniqueness, and the continuous dependence of a generalized solution upon the data of certain parabolic and hyperbolic equations with a boundary integral condition. The proof uses a functional analysis method based on a priori estimates established in nonclassical function spaces, and on the density of the range of the linear ...
Abdelfatah Bouziani
wiley   +1 more source

Regularity of a degenerate parabolic equation appearing in Vecer's unified pricing of Asian options

, 2015
Vecer derived a degenerate parabolic equation with a boundary condition characterizing the price of Asian options with generally sampled average. It is well understood that there exists a unique probabilistic solution to such a problem but it remained ...
Dong, Hongjie, Kim, Seick
core   +1 more source

On principal eigenvalues for periodic parabolic Steklov problems

Abstract and Applied Analysis, Volume 7, Issue 8, Page 401-421, 2002., 2002
Let Ω be a C2+γ domain in ℝN, N ≥ 2, 0 < γ < 1. Let T > 0 and let L be a uniformly parabolic operator Lu = ∂u/∂t − ∑i,j (∂/∂xi) (aij(∂u/∂xj)) + ∑jbj (∂u/∂xi) + a0u, a0 ≥ 0, whose coefficients, depending on (x, t) ∈ Ω × ℝ, are T periodic in t and satisfy some regularity assumptions.
T. Godoy, E. Lami Dozo, S. Paczka
wiley   +1 more source

Solution of one initial-boundary Wentzel problem for a parabolic equation with discontinuous coefficients by the boundary integral equation method

, 2017
In this article we consider the question of existence in the Holder class of the solution of the initial-boundary problem for a linear parabolic second-degree equation with discontinuous coefficients in noncylindrical domain.
B. Kopytko, Zhanneta Tsapovska
semanticscholar   +1 more source

Global existence of solutions of semilinear heat equation with nonlinear memory condition

, 2019
We consider a semilinear parabolic equation with flux at the boundary governed by a nonlinear memory. We give some conditions for this problem which guarantee global existence of solutions as well as blow up in finite time of all nontrivial solutions ...
Gladkov, Alexander, Guedda, Mohammed
core   +1 more source