講演者：Jin Feng 氏 (Department of Mathematics, The University of Kansas, USA)
時間: 2017年 7月14日 (金) 16:30～17:30(16:00からtea)
題目: “ A renormalized viscosity solution for Hamilton-Jacobi equations in metric space ”
The background model we have in mind is an infinite collection of Newtonian attractive particles. We are interested in establishing a well posedness theory for the Hamilton-Jacobi partial differential equations. The strong attractive interaction causes singularities of the state. We make use of the Maupertuis principle in this context to define a change of coordinate to auto zoom in or zoom out. We will also explore techniques from the weak KAM theory and define new barrier functions for the uniqueness part of the theory (the comparison principle). All of this is achieved at a much more general setup by considering the problem as a special case of PDEs defined in geodesic metric space.