Backward Uniqueness for Parabolic Equations

نویسندگان

  • L. Escauriaza
  • G. Seregin
چکیده

It is shown that a function u satisfying |∂t + u| M (|u| + |∇u|), |u(x, t)| MeM|x| in (R \ BR) × [0, T ] and u(x, 0) = 0 for x ∈ R \ BR must vanish identically in R \ BR × [0, T ].

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Existence, 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 کامل

Backward uniqueness of stochastic parabolic like equations driven by Gaussian multiplicative noise

One proves here the backward uniqueness of solutions to stochastic semilinear parabolic equations and also for the tamed Navier–Stokes equations driven by linearly multiplicative Gaussian noises. Applications to approximate controllability of nonlinear stochastic parabolic equations with initial controllers are given. The method of proof relies on the logarithmic convexity property known to hol...

متن کامل

Backward parabolic Ito equations and second fundamental inequality

Existence, uniqueness, and a priori estimates for solutions are studied for stochastic parabolic Ito equations. An analog of the second fundamental inequality and the related existence theorem are obtained for backward stochastic parabolic Ito equation. AMS 1991 subject classification: Primary 60J55, 60J60, 60H10. Secondary 34F05, 34G10.

متن کامل

Strong Uniqueness for an SPDE via backward doubly stochastic differential equations

We prove strong uniqueness for a parabolic SPDE involving both the solution v(t, x) and its derivative ∂xv(t, x). The familiar YamadaWatanabe method for proving strong uniqueness might encounter some difficulties here. In fact, the Yamada-Watanabe method is essentially one dimensional, and in our case there are two unknown functions, v and ∂xv. However, Pardoux and Peng’s method of backward dou...

متن کامل

Backward Uniqueness and the Existence of the Spectral Limit for Some Parabolic Spdes

ABSTRACT. The aim of this article is to study the asymptotic behaviour for large times of solutions to a certain class of stochastic partial differential equations of parabolic type. In particular, we will prove the backward uniqueness result and the existence of the spectral limit for abstract SPDEs and then show how these results can be applied to some concrete linear and nonlinear SPDEs. For...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2003