Journal
JOURNAL OF EVOLUTION EQUATIONS
Volume 21, Issue 4, Pages 5037-5053Publisher
SPRINGER BASEL AG
DOI: 10.1007/s00028-021-00740-z
Keywords
Observability inequality; Degenerate hyperbolic equation; Carleman estimate
Categories
Funding
- Istituto Nazionale di Alta Matematica (INdAM), through the GNAMPA Research Project
- [JP15H05740]
- [JP20J11497]
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In this paper, an observability inequality for a degenerate transport equation with time-dependent coefficients is proven. A local in time Carleman estimate is introduced for the degenerate equation, which is then applied to derive a global in time observability inequality along with an energy estimate.
In this paper, we prove an observability inequality for a degenerate transport equation with time-dependent coefficients. First we introduce a local in time Carleman estimate for the deeenerate equation, then we apply it to obtain a global in time observability inequality by using also an energy estimate.
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