Existence and approximation of nonlocal optimal design problems driven by parabolic equations

Distributed Solution of Optimal Control Problems Governed by Parabolic Equations

We present a spatial domain decomposition (DD) method for the solution of discretized parabolic linear–quadratic optimal control problems. Our DD preconditioners are extensions of Neumann-Neumann DD methods, which have been successfully applied to the solution of single elliptic partial differential equations and of linear–quadratic optimal control problems governed by elliptic equations. We us...

existence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types

بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی ‎‏بیان شد‎‎‏ه اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Nonlocal Problems for Parabolic Inclusions

Let be a an open bounded domain in R , N 2; with a smooth boundary @ ; and T > 0. De…ne D = (0; T ) and = @ [0; T ]: In this paper we are concerned with the existence of solutions of the following parabolic inclusion ut + Lu 2 F (x; t; u), (x; t) 2 D; u(x; t) = 0; (x; t) 2 subjected to the nonlocal condition u(x; 0) = R T 0 g(x; t; u(x; t))dt for x 2 : We provide su¢ cient conditions on L; F; g...

Regularity results for nonlocal equations by approximation

We obtain C regularity estimates for nonlocal elliptic equations that are not necessarily translation invariant using compactness and perturbative methods and our previous regularity results for the translation invariant case.