Seminar on nonlinear problems of PDE and mathematical physics (chief A. E. Shishkov)
Localization properties of boundary regimes with infinite peaking as t tends to T<∞ for some parabolic equations, admitting barrier technique, were studied since 60-th of 20 century by A.A.Samarskii,I.M.Sobol', S.P.Kurdyunov,V.A.Galaktionov,B.H.Gilding, M.A.Herrero, A.S.Kalashnikov,,C.Cortazar,M.Elgueta and other. In 1999 A.E Shishkov proposed new approach to the study of mentioned problem, which do not use any variant of barrier technique (any comparison theorems) and is based on some adaptation of local energy estimates method. In the series of papers of V.A.Galaktionov and A.E. Shishkov mentioned approach was adapted for obtaining of sharp localization conditions of boundary regimes with strong peaking for higher order quasi-linear parabolic PDE. In present talk we will discuss new results about sharp upper estimates of final profile of solutions of parabolic PDE near to the blow-up time of boundary data, which generate localized peaking regime.
Differential equations not resolved with respect to the derivatives and their applications to mathematical economics
The talk is devoted to the qualitative study of differential equations not resolved with respect to the derivatives. One of the main features of such equations is the existence of singular points, where the standard conditions of the existence and the uniqueness of solution are violated. Equations of this type find applications in various fields of technology (for example, in electrical engineering) and in mathematical economics.
Professor of the Russian Academy of Sciences Galina Lazareva will visit the S.M. Nikol’skii Mathematical Institute with a series of lectures on mathematical modeling of physical processes
During lectures for students and professors of the Mathematical Institute the following questions will be discussed in detail: simulation of low-temperature multicomponent plasmas in a target trap; Two-dimensional numerical simulation of tungsten melting in exposure to pulsed electron beam; simulation of seismic structure dynamics in a volcanic magma chamber.
Asymptotic stability of the solitons of the generalized Kawahara (gKW) equation
In the last talk (12, February), we proved the Nonlinear Liouville Property for the gKW equation. Using this result, we will show the asymptotic stability of the soliton solutions of gKW equation. Namely, we prove the following property: if the global solution of gKW is close to a soliton at initial time, then this solution converges (in some sense) to a soliton.
On ellipticity of operators, associated with metaplectic group
The first part of the talk is devoted to defining the metaplectic group, presenting its properties and applications. In the second part, we define the symbol of considered operators and establish the finiteness theorem.