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...

The aim of this paper is to present strong maximum principles for infinite systems of parabolic differential-functional inequalities with nonstandard initial inequalities with sums in relatively arbitrary (n+1)-dimensional time-space sets more general than the cylindrical domain.

Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Nahm transform for parabolic connections. . . . . . . . . . . . 3 2. Laplace transform without parabolic structure . . . . . . . 8 3. Meromorphic connections and D-modules. . . . . . . . . . . . 10 4. Minimal parabolic Laplace transform. . . . . . . . . . . . . . . . . 14 5. Proof – outline....

We discuss the construction and estimates of the Green and Poisson functions associated with a parabolic second order integro-differential operator with Wentzell boundary conditions.

In this paper we consider models built in [3] for short-term, mean-term and long-term morphodynamics of dunes and megariples. We give an existence and uniqueness result for long term dynamics of dunes. This result is based on a time-space periodic solution existence result for degenerated parabolic equation that we set out. Finally the mean-term and long-term models are homogenized.

Stability plays a central role in arithmetic. In this article, we explain some basic ideas and present certain constructions for such studies. There are two aspects: namely, general Class Field Theories for Riemann surfaces using semistable parabolic bundles & for p-adic number fields using what we call semi-stable filtered (φ,N;ω)-modules; and non-abelian zeta functions for function fields ove...