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A quantitative internal unique continuation for stochastic parabolic equations
1. | School of Mathematics, Sichuan Normal University, Chengdu, 610068, China |
References:
[1] |
L. Escauriaza, Carleman inequalities and the heat operator, Duke Math. J., 104 (2000), 113-127.
doi: 10.1215/S0012-7094-00-10415-2. |
[2] |
L. Escauriaza and L. Vega, Carleman inequalities and the heat operator II, Indiana U. Math. J., 50 (2001), 1149-1169.
doi: 10.1512/iumj.2001.50.1937. |
[3] |
V. Isakov, Carleman type estimates in an anisotropic case and applications, J. Differential Equations, 105 (1993), 217-238.
doi: 10.1006/jdeq.1993.1088. |
[4] |
H. Li and Q. Lü, A quantitative boundary unique continuation for stochastic parabolic equations, J. Math. Anal. Appl., 402 (2013), 518-526.
doi: 10.1016/j.jmaa.2013.01.038. |
[5] |
F. H. Lin, A uniqueness theorem for parabolic equations, Comm. Pure Appl. Math., 43 (1990), 127-136.
doi: 10.1002/cpa.3160430105. |
[6] |
Q. Lü, Observability estimate for stochastic Schrödinger equations and its applications, SIAM J. Control Optim., 51 (2013), 121-144.
doi: 10.1137/110830964. |
[7] |
Q. Lü, Observability estimate and state observation problems for stochastic hyperbolic equations, Inverse Problems, 29 (2013), 095011, 22 pp.
doi: 10.1088/0266-5611/29/9/095011. |
[8] |
C. C. Poon, Unique continuation for parabolic equations, Comm. Partial Differential Equations, 21 (1996), 521-539.
doi: 10.1080/03605309608821195. |
[9] |
J.-C. Saut and B. Scheurer, Unique continuation for soome evolution equations, J. Differential Equations, 66 (1987), 118-139.
doi: 10.1016/0022-0396(87)90043-X. |
[10] |
C. D. Sogge, A unique continuation theorem for second order parabolic differential operators, Ark. Mat., 28 (1990), 159-182.
doi: 10.1007/BF02387373. |
[11] |
S. Tang and X. Zhang, Null controllability for forward and backward stochastic parabolic equations, SIAM J. Control Optim., 48 (2009), 2191-2216.
doi: 10.1137/050641508. |
[12] |
H. Yamabe, A unique continuation theorem of a diffusion equation, Ann. Math., 69 (1959), 462-466.
doi: 10.2307/1970194. |
[13] |
X. Zhang, Unique continuation for stochastic parabolic equations, Differential Integral Equations, 21 (2008), 81-93. |
[14] |
E. Zuazua, Controllability and observability of partial differential equations: Some results and open problems, in Handbook of Differential Equations: Evolutionary Differential Equations. Vol. III, Handb. Differ. Equ., Elsevier/North-Holland, Amsterdam, 2007, 527-621.
doi: 10.1016/S1874-5717(07)80010-7. |
[15] |
C. Zuily, Uniqueness and Non-Uniqueness in the Cauchy Problem, Progress in Mathematics, 33, Birkhäuser, Boston, 1983.
doi: 10.1007/978-1-4899-6656-8. |
show all references
References:
[1] |
L. Escauriaza, Carleman inequalities and the heat operator, Duke Math. J., 104 (2000), 113-127.
doi: 10.1215/S0012-7094-00-10415-2. |
[2] |
L. Escauriaza and L. Vega, Carleman inequalities and the heat operator II, Indiana U. Math. J., 50 (2001), 1149-1169.
doi: 10.1512/iumj.2001.50.1937. |
[3] |
V. Isakov, Carleman type estimates in an anisotropic case and applications, J. Differential Equations, 105 (1993), 217-238.
doi: 10.1006/jdeq.1993.1088. |
[4] |
H. Li and Q. Lü, A quantitative boundary unique continuation for stochastic parabolic equations, J. Math. Anal. Appl., 402 (2013), 518-526.
doi: 10.1016/j.jmaa.2013.01.038. |
[5] |
F. H. Lin, A uniqueness theorem for parabolic equations, Comm. Pure Appl. Math., 43 (1990), 127-136.
doi: 10.1002/cpa.3160430105. |
[6] |
Q. Lü, Observability estimate for stochastic Schrödinger equations and its applications, SIAM J. Control Optim., 51 (2013), 121-144.
doi: 10.1137/110830964. |
[7] |
Q. Lü, Observability estimate and state observation problems for stochastic hyperbolic equations, Inverse Problems, 29 (2013), 095011, 22 pp.
doi: 10.1088/0266-5611/29/9/095011. |
[8] |
C. C. Poon, Unique continuation for parabolic equations, Comm. Partial Differential Equations, 21 (1996), 521-539.
doi: 10.1080/03605309608821195. |
[9] |
J.-C. Saut and B. Scheurer, Unique continuation for soome evolution equations, J. Differential Equations, 66 (1987), 118-139.
doi: 10.1016/0022-0396(87)90043-X. |
[10] |
C. D. Sogge, A unique continuation theorem for second order parabolic differential operators, Ark. Mat., 28 (1990), 159-182.
doi: 10.1007/BF02387373. |
[11] |
S. Tang and X. Zhang, Null controllability for forward and backward stochastic parabolic equations, SIAM J. Control Optim., 48 (2009), 2191-2216.
doi: 10.1137/050641508. |
[12] |
H. Yamabe, A unique continuation theorem of a diffusion equation, Ann. Math., 69 (1959), 462-466.
doi: 10.2307/1970194. |
[13] |
X. Zhang, Unique continuation for stochastic parabolic equations, Differential Integral Equations, 21 (2008), 81-93. |
[14] |
E. Zuazua, Controllability and observability of partial differential equations: Some results and open problems, in Handbook of Differential Equations: Evolutionary Differential Equations. Vol. III, Handb. Differ. Equ., Elsevier/North-Holland, Amsterdam, 2007, 527-621.
doi: 10.1016/S1874-5717(07)80010-7. |
[15] |
C. Zuily, Uniqueness and Non-Uniqueness in the Cauchy Problem, Progress in Mathematics, 33, Birkhäuser, Boston, 1983.
doi: 10.1007/978-1-4899-6656-8. |
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