Singular Problems, Blow-up, and Regimes with Peaking in Nonlinear PDEs
Main topics of the conference: Blow-up and singularities for nonlinear PDEs; Peaking regimes in nonlinear evolution equations; Large solutions of nonlinear elliptic and parabolic equations and systems;
Mathematical modelling in biomedicine
The conference will present the state of the art in mathematical modelling in biomedicine including cardiovascular diseases, cancer modelling, mathematical oncology. Methods of modelling and mathematical analysis of the corresponding models will also be discussed.
Seminar on nonlinear problems of PDE and mathematical physics
Using the Peakons (the exponential function) we will construct a family of the Degasperis-Procesi type's equations for which the Peakons is a solitary wave traveling with the velocity c^(a-1). In the case a=2 we recover the quadratic Degasperis-Procesi equation and recall that Lin-Liu-K prove the orbital stability of the Peakons. In the case a=3 we will construct a fourth order stable evolution system (definition during the talk) with the cubic Degasperis-Procesi equation. Next, we will prove that the second order stable evolution system is equivalent to the Isaac Newton Force. Finally, we will make a numerical application constructed around the egyptian cubit.
Scientific seminar on functional analysis and its applications under the guidance of A.V. Arutyunov, V.I. Burenkov and M. L. Goldman and V.N. Rozova
We will consider the problem of obtaining order-sharp integral estimates for the norms of restrictions of operators on the cones of functions with monotonicity properties. A discretization method will be discussed that takes into account the monotonicity of functions and allows to receive answers in a discrete form. To return to integral forms, the techniques of anti- discretization is used
Scientific seminar on the differential and functional differential equation under the guidance of Professor A.L. Skubachevskii
We study the Dirichlet problem for a functional differential equation containing shifted and contracted argument under the Laplacian sign. We establish conditions for the unique solvability and demonstrate also that the problem may have an infinite dimensional solution manifold.
Scientific seminar on the differential and functional differential equation under the guidance of prof. Sternin B. Yu. and prof. Savin A.Yu
Topic: Тhe spectral Flow of a family of Toeplitz operators.
A series of lectures on mathematical methods and theoretical physics
Andreas Wipf, Professor of Friedrich-Schiller-University, will visit the S.M. Nikol’skii Mathematical Institute with a series of lectures on mathematical methods and theoretical physics.