Seminar “Existence, asymptotics and Lyapunov's stability of solutions of periodic parabolic boundary-value problems for Tikhonov-type systems”
On 26 December at 18:00 p.m. (Moscow time)
A seminar on nonlinear problems of PDE and mathematical physics “Existence, asymptotics and Lyapunov’s stability of solutions of periodic parabolic boundary-value problems for Tikhonov-type systems” will be held at RUDN University.
Speaker: Professor Nikolay Nefedov, Faculty of Physics of Moscow Lomonosov State University.
We consider a periodic parabolic singularly perturbed boundary value problem for the Tikhonov system: a singularly perturbed system with fast and slow equations. An asymptotic approximation of the solution to the problem is constructed, conditions for the existence of a solution and its asymptotic stability according to Lyapunov are obtained for these solutions as solutions to the corresponding initial-boundary value problems for this system, both in the case of various types of quasi-monotonicity and in the case of its violation. The results are generalized to initial-boundary value parabolic problems, including problems with quadratic nonlinearities (the so-called KPZ diffusion-advection reaction systems).