We show existence of a unique, regular global solution of the parabolic-elliptic system ut + f(t, x, u)x + g(t, x, u) + Px = (a(t, x)ux)x and −Pxx + P = h(t, x, u, ux) + k(t, x, u) with initial data u|t=0 = u0. Here inf(t,x) a(t, x) > 0. Furthermore, we show that the solution is stable with respect to variation in the initial data u0 and the functions f , g etc. Explicit stability estimates are...

We present some new relations between the pseudo-derivatives and parabolic epiderivatives recently introduced by Rockafellar, and also its infinite dimensional counterparts. Significant extensions of the most important known results are proven, which further clarify the range of applicability of this new theory.

We consider a class of ultra-parabolic Kolmogorov-type operators satisfying the Hörmander’s condition. We prove an intrinsic Taylor formula with global and local bounds for the remainder given in terms of the norm in the homogeneous Lie group naturally associated to the differential operator.

This paper expands the earlier paper [30] and presents foundation for a systematic treatment of three main (elliptic, parabolic and hyperbolic) types of analytic function theory based on the representation theory of SL2(R) group. We describe here geometries of corresponding domains. The principal rôle is played by Clifford algebras of matching types. In this paper we also generalise the Fillmor...

We prove the conjecture of Frenkel, Kac and Wakimoto on the existence of two-sided BGG resolutions of G-integrable admissible representations of affine Kac-Moody algebras at fractional levels. As an application we establish the semi-infinite analogue of the generalized Borel-Weil theorem for minimal parabolic subalgebras which enables an inductive study of admissible representations.

We investigate the uniqueness of limit solutions for a free boundary problem in heat propagation that appears as a limit of a parabolic system that arises in flame propagation.