This work was intended as an attempt to investigate a simple mathematical model cell. This model represents a problem with free boundary for system of two differential equations, one of which is parabolic and another one ...

A model of a strongly inhomogeneous medium with simultaneous perturbation of the rigidity and mass density is studied. The medium has strongly contrasting physical characteristics in two parts with the ratio of rigidities ...

In the paper I solve the problem of a multiple spectrum without any artificial conditions imposed and obtain whole asymptotic expansions for eigenvalues and eigen-functions of the general smooth boundary-value problem for ...

In this paper we study the existence of global compact attractors for nonlinear parabolic equations of reaction-diffusion type. The studied equations are generated by a difference of subdifferential maps and are not assumed ...

In a bounded domain with infinitely increasing quantity of infinitesimal holes whose asymptotic behaviour is described formally, the homogeneous Dirichlet problem for the equation with additional power nonlinearity on the ...

In this note we study a semilinear elliptic boundary value problem of one parameter dependence which arises in population genetics, having nonlinear boundary conditions. For some cases of sign indefinite weights, we ...

We obtain the applications of approach [2, 5, 6] to the high order regularity of solutions to the parabolic Cauchy problem with globally non-Lipschitz coeffcients growing at the in nity of a noncompact manifold. In comparison ...