On quantitative uniqueness for parabolic equations
We consider the quantitative uniqueness properties for a parabolic type equation ut−Δu=w(x,t)⋅∇u+v(x,t)u, when v∈Ltp2Lxp1 and w∈Ltq2Lxq1, with a suitable range for exponents p1, p2, q1, and q2. We prove a strong unique continuation property and provide a pointwise in time observability estimate....
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| Published in | Journal of Differential Equations Vol. 341; pp. 438 - 480 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
25.12.2022
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| Online Access | Get full text |
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| Summary: | We consider the quantitative uniqueness properties for a parabolic type equation ut−Δu=w(x,t)⋅∇u+v(x,t)u, when v∈Ltp2Lxp1 and w∈Ltq2Lxq1, with a suitable range for exponents p1, p2, q1, and q2. We prove a strong unique continuation property and provide a pointwise in time observability estimate. |
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| ISSN: | 0022-0396 1090-2732 |
| DOI: | 10.1016/j.jde.2022.09.011 |