Time：9:00-11:00, Friday, July 12 2024
Venue：E4-233, Yungu Campus
Host： Zipeng Wang, ITS
Speaker：Alberto Bressan, The Pennsylvania State University
Biography：Professor Bressan received his Ph. D. from the University of Calorado in 1982. Earlier in his career, he made certain important contributions to the theory of hyperbolic conservation laws and was invited to give a plenary talk at International Congress of Mathematicians 2002 in Beijing. He won a number of distinguished awards including Bôcher Memorial Price 2008, Analysis of Partial Differential Equations, 2007. He became a member of the Royal Norwegian Society of Science and Letters in 2011 and a fellow of the American Mathematical Society in 2012.
Title：A time dependent Queen Dido's problem
Abstract: According to classical tradition, Queen Dido's problem (approx. 814 BC) requires to enclose a portion of land of maximum area next to the sea shore, using a thread of given length. This is considered to be the oldest problem in the Calculus of Variations.
After a brief historical introduction, in this talk I shall discuss a new class of time-dependent problems, in a similar vein.
A set V(t), modeling the region contaminated by an invasive biological species, expands with unit speed in all directions.
Its growth can be controlled by clearing a region of area M per unit time.
Control strategies are sought, which shrink the set V(t) to the empty set in minimum time, or minimize its area at a terminal time T.
To find optimal strategies one seeks to minimize the perimeters of the sets V(t), among sets with the same area, for every time t.
Existence and properties of optimal strategies will be discussed, together with some open questions.
