Homogenization of forward-backward parabolic equations
نویسنده
چکیده
We study the homogenization of the equation R(εx) ∂uε ∂t −∆uε = f , where R is a periodic function which may vanish or change sign, with appropriate initial/final conditions. The main tool is a compactness result for sequences of functions which have bounded norms in the spaces associated to the problems.
منابع مشابه
Auxiliary Sdes for Homogenization of Quasilinear Pdes with Periodic Coefficients
We study the homogenization property of systems of quasi-linear PDEs of parabolic type with periodic coefficients, highly oscillating drift and highly oscillating nonlinear term. To this end, we propose a probabilistic approach based on the theory of forward–backward stochastic differential equations and introduce the new concept of " auxiliary SDEs. " 1. Introduction and assumptions.
متن کاملExistence, duality, and causality for backward parabolic Ito equations
We study existence, uniqueness, and a priori estimates for solutions for backward parabolic Ito equations in domains with boundary. The proofs are based duality between forward and backward equations. This duality is used also to establish that backward parabolic equations have some causality (more precisely, some anti-causality). AMS 1991 subject classification: Primary 60J55, 60J60, 60H10. Se...
متن کاملForward – backward stochastic di erential equations with nonsmooth coe cients
Solvability of forward–backward stochastic di erential equations with nonsmooth coe cients is considered using the Four-Step Scheme and some approximation arguments. For the onedimensional case, the existence of an adapted solution is established for the equation which allows the di usion in the forward equation to be degenerate. As a byproduct, we obtain the existence of a viscosity solution t...
متن کاملControllability of 1-d Coupled Degenerate Parabolic Equations
This article is devoted to the study of null controllability properties for two systems of coupled one dimensional degenerate parabolic equations. The first system consists of two forward equations, while the second one consists of one forward equation and one backward equation. Both systems are in cascade, that is, the solution of the first equation acts as a control for the second equation an...
متن کامل