We consider the transport equation in a bounded domain. First, we prove a Carleman estimate for solutions of finite energy with piecewise continuous weight functions. Then, under a further condition we prove an energy estimate which in turn yields an observability inequality. Our results are motivated by applications to inverse problems.
Observability inequalities for transport equations through Carleman estimates / Cannarsa, Piermarco; Floridia, G.; Yamamoto, Masahiro. - Vol. 32:(2019), pp. 69-87. [10.1007/978-3-030-17949-6_4]
Observability inequalities for transport equations through Carleman estimates
G. Floridia;
2019-01-01
Abstract
We consider the transport equation in a bounded domain. First, we prove a Carleman estimate for solutions of finite energy with piecewise continuous weight functions. Then, under a further condition we prove an energy estimate which in turn yields an observability inequality. Our results are motivated by applications to inverse problems.File in questo prodotto:
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