Backward uniqueness of Kolmogorov operators
نویسندگان
چکیده
منابع مشابه
Backward Uniqueness for Parabolic Equations
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 ].
متن کاملBackward uniqueness for the heat equation
According to Gurarii and Matsaev [5], these properties are equivalent, but no proof was ever published. Here is a summary of known results. When n = 1, both properties hold if and only if D is a bounded interval. For PII this is evident, for PI this follows from the results of Tychonov [7]. When n = 2, and D is an angular sector {z : | arg z| < α}, the property PII holds if and only if α < 45◦....
متن کاملThe Navier-Stokes equations and backward uniqueness
We consider the open problem of regularity for L3,∞-solutions to the Navier-Stokes equations. We show that the problem can be reduced to a backward uniqueness problem for the heat operator with lower order terms. 1991 Mathematical subject classification (Amer. Math. Soc.): 35K, 76D.
متن کاملBackward uniqueness for the heat equation
According to Gurarii and Matsaev [5], these properties are equivalent, but no proof was ever published. Here is a summary of known results. When n = 1, both properties hold if and only if D is a bounded interval. For PII this is evident, for PI this follows from the results of Tychonov [7]. When n = 2, and D is an angular sector {z : | arg z| < α}, the property PII holds if and only if α < 45◦....
متن کاملNonlocal transformations of Kolmogorov equations into the backward heat equation
We extend and solve the classical Kolmogorov problem of finding general classes of Kolmogorov equations that can be transformed to the backward heat equation. These new classes include Kolmogorov equations with time-independent and time-dependent coefficients. Our main idea is to include nonlocal transformations. We describe a step-by-step algorithm for determining such transformations. We also...
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ژورنال
عنوان ژورنال: Methods and Applications of Analysis
سال: 2013
ISSN: 1073-2772,1945-0001
DOI: 10.4310/maa.2013.v20.n1.a5