TY - JOUR
T1 - Observability inequalities for degenerate transport equations
AU - Floridia, Giuseppe
AU - Takase, Hiroshi
N1 - Funding Information:
This work was supported by Grant-in-Aid for Scientific Research (S) Grant Number JP15H05740, Grant-in-Aid for JSPS Fellows Grant Number JP20J11497, and Istituto Nazionale di Alta Matematica (INAM), through the GNAMPA Research Project 2020, titled “Problemi inversi e di controllo per equazioni di evoluzione e loro applicazioni,” coordinated by the first author. Moreover, this research was performed in the framework of the French-German-Italian Laboratoire International Associé (LIA), named COPDESC, on Applied Analysis, issued by CNRS, MPI, and INAM, during the INAM Intensive Period-2019, “Shape optimization, control and inverse problems for PDEs,” held in Napoli in May–June–July 2019. The authors thank Prof. Piermarco Cannarsa and Prof. Masahiro Yamamoto for the useful and interesting discussions about the topics of this paper.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
PY - 2021/12
Y1 - 2021/12
N2 - 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 degenerate equation, then we apply it to obtain a global in time observability inequality by using also an energy estimate.
AB - 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 degenerate equation, then we apply it to obtain a global in time observability inequality by using also an energy estimate.
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U2 - 10.1007/s00028-021-00740-z
DO - 10.1007/s00028-021-00740-z
M3 - Article
AN - SCOPUS:85114814116
SN - 1424-3199
VL - 21
SP - 5037
EP - 5053
JO - Journal of Evolution Equations
JF - Journal of Evolution Equations
IS - 4
ER -