Results 21 to 30 of about 712 (65)
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
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A nonlinear parabolic problem with singular terms and nonregular data [PDF]
, 2019 We study existence of nonnegative solutions to a nonlinear parabolic boundary value problem with a general singular lower order term and a nonnegative measure as nonhomogeneous datum, of the form $$ \begin{cases} \dys u_t - \Delta_p u = h(u)f ...
Oliva, Francescantonio +1 more
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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
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A probabilistic solution to the Stroock-Williams equation [PDF]
, 2014 We consider the initial boundary value problem \begin{eqnarray*}u_t=\mu u_x+\tfrac{1}{2}u_{xx}\qquad (t>0,x\ge0),\\u(0,x)=f(x)\qquad (x\ge0),\\u_t(t,0)=\nu u_x(t,0)\qquad (t>0)\end{eqnarray*} of Stroock and Williams [Comm. Pure Appl. Math. 58 (2005) 1116-
Peskir, Goran
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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
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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
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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
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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
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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
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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