[STAR Seminars] Wed Feb 11 - Rahma Yasmina Moulay Hachemi
Dear all, Join us for our upcoming talk in the STAR seminar<https://www.mn.uio.no/math/english/research/projects/storm/events/seminars/star-online-seminars/> series on Wednesday, February 11th, from 11:00 to 12:00 (Oslo time). As always, the talk will take place in a hybrid format: participants in Oslo can attend the talk in Room 723 in Niels Henrik Abels hus, whereas the international audience will be able to follow the talk via Zoom<https://uio.zoom.us/j/61970286852>. The speaker is Rahma Yasmina Moulay Hachemi (University of Saida Dr. Moulay Tahar) with the talk: Title: The time-fractional stochastic heat equation driven by time-space white noise Abstract: We study the stochastic time-fractional stochastic heat equation: ∂α/∂tα Y(t, x) = λΔY (t, x) + σ W(t, x); (t, x) ∈ (0,∞) × Rd , (0.1), where d ∈ N = {1, 2, ...} and ∂α/∂tα is the Caputo derivative of order α ∈ (0, 2), and λ > 0 and σ ∈ R are given constants. We consider the equation in the sense of distribution, and we find an explicit expression for the S-valued solution Y (t, x), where S is the space of tempered distributions. Following the terminology of Y. Hu [1], we say that the solution is mild if Y (t, x) ∈ L2(P) for all t, x. It is well-known that in the classical case with α = 1, the solution is mild if and only if the space dimension d = 1. We prove that if α ∈ (1, 2) the solution is mild if d = 1 or d = 2. If α < 1 we prove that the solution is not mild for any d. [1] Hu, Yaozhong (2019): Some recent progress on stochastic heat equations. Acta Mathematica Scientia 39B(3); 874-914 We are looking forward to seeing you! Best regards, Giulia, Leonardo, Pere, and David
partecipanti (1)
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Leonardo Tarquini