期刊
PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES
卷 39, 期 2, 页码 227-274出版社
KYOTO UNIV
DOI: 10.2977/prims/1145476103
关键词
Carleman inequality; Sobolev space of negative order; unique continuation; exact controllability; duality; semilinear parabolic equation
类别
We prove Carleman inequalities for a second order parabolic equation when the coefficients are not bounded and norms of right hand sides are taken in the Sobolev space L-2 (0, T; W-2(-l) (Omega)), l epsilon [0, 1]. Our Carleman inequality yields the unique continuation for L-2-solutions. We further apply these inequalities to the global exact zero controllability of a semilinear parabolic equation whose semilinear term also contains derivatives of first order of solutions and is of sub-linear growth at the infinity.
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