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 ...

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 show how the use of nonlinear symmetries of higher-order derivatives allows one to study the regularity of solutions of nonlinear differential equations in the case where the classical Cauchy-Liouville-Picard scheme is ...

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 ...

It is shown that the geometrically correct investigation of regularity of nonlinear differential flows on manifolds and related parabolic equations requires the introduction of a new type of variations with respect to the ...