We study the dependence with respect to the initial data for solutions of diffusion equations with globally non-Lipschitz coefficients on noncompact manifolds. Though the metric distance may be not everywhere twice ...

We find sufficient conditions on coefficients of diffusion equation on noncompact manifold, that guarantee non-explosion of solutions in a finite time. This property leads to the existence and uniqueness of solutions for ...

We study the regularity problems for unbounded spin systems of anharmonic oscillators, that approximate multi-dimensional Euclidean field theories. The main attention is paid to the effect of anharmonism on the C∞-regularity ...

This paper is aimed to discuss an intrinsic effect on the presence of the certain gap between the boundedness and continuity topologies for derivatives of infinite dimensional semigroups that describe evolution of unbounded ...

Below we demonstrate how the C^∞-regular properties of heat dynamics with non-unit nonlinear diffusion coefficient can be studied. We consider an infinite dimensional model, describing evolution of unbounded lattice spins ...