Date: Mondays, 16:00 ~ (90 min. ~ 120 min.)
Place: Rm. 453, Mathematics Bldg, Nagoya University
Organizers: Mitsuru Sugimoto, Toshiaki Hishida, Kotaro Tsugawa, Jun Kato, Yutaka Terasawa
2018 / 2019
We consider some inverse acoustic scattering problems. For the purpose, we derive the factorization method, which is a sampling method for solving certain kinds of inverse problems where the shape and location of unknown objects have to be reconstructed. Here, we introduce new results related to the factorization method.
We study the Cauchy problem of the linear damped wave equation and give sharp $L^p$-$L^q$ estimates of the solution. This is an improvement of the so-called Matsumura estimates. Moreover, as its application, we consider the nonlinear problem with slowly decaying initial data, and determine the critical exponent. In particular, we prove that the small data global existence holds in the critical case if the initial data does not belong to $L^1$. This talk is based on a joint work with Masahiro Ikeda (RIKEN), Mamoru Okamoto (Shinshu University), and Takahisa Inui (Osaka University).