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3pm Monica Musso (Bath) Singularity formation in critical parabolic equations
Abstract (ES): In this talk I will discuss some recent constructions of blow-up solutions for a Fujita type problem for power related to the critical Sobolev exponent. Both finite type blow-up (of type II) and infinite time blow-up are considered. This research program is in collaboration with C. Cortazar, M. del Pino and J. Wei.
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4.30pm Vitaly Moroz (Swansea) Thomas-Fermi type models of external charge screening in graphene
Abstract : Graphene is a recently discovered material which consists of exactly one atomic layer of carbon. We discuss density functional theories of Thomas-Fermi and Thomas-Fermi-von Weizsacker type which describe the response of a single layer of graphene to an external electric charge. Mathematically, this amounts to the analysis of two nonlocal variational problems which involve Coulombic terms and a Hardy type potential. We formulate variational setting in which the proposed energy functionals admit minimizers. The associated Euler-Lagrange equations are also obtained, and uniqueness and regularity of the minimizers are proved under some conditions. In addition, we discuss the decay rate (screening) of the minimizers and describe several open problems.
Joint work with J. Lu (Duke) and C. Muratov (NJIT)