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Backward uniqueness for the heat operator in a half-space
Author(s):
L.
Escauriaza;
G.
Seregin;
V.
Sverák
Original publication:
Algebra i Analiz,
tom 15
(2003),
vypusk 1.
Journal:
St. Petersburg Math. J.
15
(2004),
139-148.
MSC (2000):
Primary 35K10
Posted:
December 31, 2003
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Abstract:
A backward uniqueness result is proved for the heat operator with variable lower order terms in a half-space. The main point of the result is that the boundary conditions are not controlled by the assumptions.
References:
-
- [1]
- L. Escauriaza, Carleman inequalities and the heat operator, Duke Math. J. 104 (2000), no. 1, 113-127. MR 2001m:35135
- [2]
- L. Escauriaza and F. J. Fernández, Unique continuation for parabolic operators (to appear).
- [3]
- L. Escauriaza, G. Seregin, and V. Sverák, On backward uniqueness for parabolic equations, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 288 (2002), 100-103. MR 2003i:35225
- [4]
- -, On backward uniqueness for parabolic equations, Arch. Rational Mech. Anal. (to appear).
- [5]
- L. Escauriaza and L. Vega, Carleman inequalities and the heat operator. II, Indiana Univ. Math. J. 50 (2001), 1149-1169. MR 2003b:35088
- [6]
- L. Hörmander, Linear partial differential operators, Grundlehren Math. Wiss., vol. 116, Springer-Verlag, Berlin, etc., 1963. MR 28:4221
- [7]
- O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva, Linear and quasilinear equations of parabolic type, ``Nauka'', Moscow, 1967; English transl., Transl. Math. Monogr., vol. 23, Amer. Math. Soc., Providence, RI, 1968. MR 39:3159a
- [8]
- S. Micu and E. Zuazua, On the lack of null-controllability of the heat equation on the half-space, Port. Math. (N.S.) 58 (2001), no. 1, 1-24. MR 2002a:93011
- [9]
- G. Seregin, Local regularity of suitable weak solutions to the Navier-Stokes equations near the boundary, J. Math. Fluid Mech. 4 (2002), no. 1, 1-29. MR 2003a:35152
- [10]
- G. Seregin and V. Sverák, The Navier-Stokes equations and backward uniqueness, Nonlinear Problems of Mathematical Physics and Related Topics. Vol. 2 (in Honor of Prof. O. A. Ladyzhenskaya), Kluwer Acad./Plenum Publ., 2002, pp. 359-370.
- [11]
- D. Tataru, Carleman estimates, unique continuation, and applications, Notes downloadable from http://math.berkeley.edu/tataru/ucp.html.
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Additional Information:
L.
Escauriaza
Affiliation:
Dipartimento di Matemáticas, UPV/EHU, Bilbao, Spain
Email:
mtpeszul@lq.ehu.es
G.
Seregin
Affiliation:
St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191011, Russia
Email:
seregin@pdmi.ras.ru
V.
Sverák
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN
Email:
sverak@math.umn.edu
DOI:
10.1090/S1061-0022-03-00806-9
PII:
S 1061-0022(03)00806-9
Keywords:
Backward uniqueness,
heat operator
Received by editor(s):
2/SEP/2002
Posted:
December 31, 2003
Copyright of article:
Copyright
2003,
American Mathematical Society
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