In this paper we prove sufficient conditions for the existence of global solutions of nonlinear functional-differential evolution equations whose linear parts are infinitesimal generators of strongly continuous and analytic semigroups. We apply the obtained results to a diffusion problem. 2000 MSC: Primary: 47J35, 34K12, Secondary: 34K90, 35K20, 35K60

Weighted composition operators appear in the study of dynamical systems and also in characterizing isometries of some classes of Banach spaces. One of the most important generalizations of weighted composition operators, are generalized weighted composition operators which in special cases of their inducing functions give different types of well-known operators like: weighted composition operat...

We establish small-time asymptotic expansions for heat kernels of hypoelliptic Hörmander operators in a neighborhood the diagonal, generalizing former results obtained particular by Métivier and Ben Arous. The coefficients our are identified terms nilpotentization underlying sub-Riemannian structure. Our approach is purely analytic relies on local global subelliptic estimates as well nature asy...

Abstract: It is proved that a general non-differentiable skew convolution semigroup associated with a strongly continuous semigroup of linear operators on a real separable Hilbert space can be extended to a differentiable one on the entrance space of the linear semigroup. A càdlàg strong Markov process on an enlargement of the entrance space is constructed from which we obtain a realization of ...