Events

The solvability of the nonlinear nonlocal problem, which is a generalization of the Bitsadze-Samarskii type problem, is considered. Theorems on sufficient conditions for the existence of a solution are formulated. In particular, we consider a non-local boundary value problem with a p-Laplacian.

We consider new classes of singularly perturbed initial- boundary value problems and periodic boundary value problems for reaction-advection-diffusion equations: Burgers type equations with quadratic and modular advection.

We consider an abstract differential equation of arbitrary order n in a Banach space. We assume that the equation contains an unknown element in the form of an inhomogeneous term.

The talk will focus on the large time asymptotic behavior of the fundamental solution of the parabolic equation for a convolution type operator. Under the assumption that the convolution kernel is integrable, decays at infinity sufficiently fast and satisfies natural ellipticity conditions, we will obtain asymptotic estimates for the fundamental solution in all space-time regions.

Elements of the theory of constitutive relations. Tangent modulus and tangential compliance. Physical linearity, tensor linearity (quasilinearity) and nonlinearity. Material functions. Rheonomic and scleronomic media. Homogeneous and heterogeneous media. Composites. Elastic bodies. Viscous liquids. Memory environments. Non-local environments.

The human placenta is a unique multi-functional organ. It is a life-support system that not only nourishes a growing fetus, but also determines his or her life-long health.

We prove continuity and Harnack`s inequality for bounded solutions of elliptic and parabolic equations with generalized Orlicz growth. These classes include the new cases of equations with (p,q)-nonlinearity and non-logarithmic growth.

We study the effects of nonlocal control of front propagation in excitable media. As a generic example we consider Nagumo equation, which is a paradigmatic model of a bistable media in which one can observe front propagation.

We prove the global existence and blow-up of solutions of an initial boundary value problem for nonlinear nonlocal parabolic equation with nonlinear nonlocal boundary condition.

We consider problems in multilevel cascade connections with a large number of light, medium and heavy concentrated masses. We give a complete classification of the limiting cases.