You are most cordially invited to Yeditepe Mathematics Department Seminars. The details of this week's talk are as follows. The seminar will be online via google meet. 

Speaker: Halit Şevki Aslan  (University of Sao Paolo)
 
Title: Lp−Lq estimates for solutions to the plate equation with mass term

Abstract: In this talk, we are going to study the following Cauchy problem for the plate equation with mass term: utt+Δ2u+u=0 if (t,x)∈(0,∞)×Rn u(0,x)=u0(x)  ut(0,x)=u1(x)  if x∈Rn. Our goal is to derive Lp−Lq estimates for the solutions to problem \eqref{eq_1} in the full range 1≤p≤q≤∞. After that, we study the associated semilinear model with power non-linearity ∣u∣α with α>1, where we apply the derived Lp−Lq estimates in the analysis of local (in time) existence of solution and for the global (in time) small data solutions.

The results of this talk are based on collaboration with Alexandre A. Junior (University of São Paulo, Ribeirão Preto, Brazil), Marcelo R. Ebert (University of São Paulo, Ribeirão Preto, Brazil), Antonio Lagioia (University of Bari, Italy).

References:

[1] M. D'Abbicco, M.R. Ebert, Lp−Lq estimates for a parameter-dependent multiplier with oscillatory and diffusive components. J. Math. Anal. Appl. {504} (2021).

[2] M. Ikeda, T. Inui, A remark on non-existence results for the semi-linear damped Klein-Gordon equations. RIMS Kôkyûroku Bessatsu B56, (2016), 11--30.

[3] B. Marshall, W. Strauss, S. Wainger, Lp−Lq estimates for the Klein-Gordon equation. J. Math. Pures Appl. 59. (1980) 417--440.

Date: Wednesday, October 30, 2024
Time: 13:00
Place: Online - Google Meet: https://meet.google.com/bii-ppma-egu 

(The seminar will be streamed in the  Mathematics-Physics Seminar room as well.)

Listing: https://researchseminars.org/seminar/7tepemathseminars