20 October, at 19:00 MSK
Theory of very singular (i.e. more singular then corresponding fundamental) nonnegative solutions is actively developing since pioneering work of H.Brezis, L.A.Peletier, D.Terman (1986) field of qualitative theory of nonlinear elliptic and parabolic equations of diffusion-absorption type.
In this talk we will discuss some new aspects of this theory, connected with the degeneration of nonlinear absorption term on some manifolds of the domain under consideration. We have obtained some sharp sufficient and necessary (even criteria for some manifolds) conditions on the character of mentioned degeneration, guaranteeing propagation or non-propagation of strong singularities of solutions along mentioned manifolds and, as a consequence, existence of very singular solutions with strong point singularity. These conditions lead to the description of different complicated singular solutions: "razor blade" solutions, large solutions and other.
Professor A.E. Shishkov ( Nikolskii Mathematical Institute of RUDN University, Moscow, Russian Federation).
Title of the talk: Propagation of strong singularities in nonlinear diffusion-absorption type equations.