Regularity theory in PDE plays an important role in the development of second-order elliptic and parabolic equations. Classical regularity estimates for elliptic and parabolic equations consist of Schauder estimates, L estimates, De Giorgi-Nash estimates, KrylovSafonov estimates, and so on. L and Schauder estimates, which play important roles in the theory of partial differential equations, are...

Some studies suggest that complex arm movements in humans and monkeys may optimize several objective functions, while others claim that arm movements satisfy geometric constraints and are composed of elementary components. However, the ability to unify different constraints has remained an open question. The criterion for a maximally smooth (minimizing jerk) motion is satisfied for parabolic tr...

In the first part of this paper, we study abstract parabolic evolution equations involving Banach space-valued measures. These results are applied in the second part to second-order parabolic systems under minimal regularity hypotheses on the coefficients. DOI: https://doi.org/10.1007/s10958-005-0376-8 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi....

It is well known that for many semilinear parabolic equations there is a global attractor which has a cell complex structure with finite dimensional cells. Additionally, many semilinear parabolic equations have equilibria with finite dimensional unstable manifolds. In this article, these results are unified to show that for a specific parabolic equation on an unbounded domain, the space of hete...

Methods used in parabolic refraction-diiraction models for computing the evolution of monochromatic waves in the nearshore zone are used to construct a model for spectral wave conditions. The two dimensional spectrum is divided into discrete wave components and the individual wave components are computed simultaneously in the domain using parabolic models for each wave component. Statistical qu...

We establish optimal order a priori error estimates for implicit– explicit BDF methods for abstract semilinear parabolic equations with timedependent operators in a complex Banach space setting, under a sharp condition on the non-self-adjointness of the linear operator. Our approach relies on the discrete maximal parabolic regularity of implicit BDF schemes for autonomous linear parabolic equat...

This paper deals with a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system. Boundedness, stabilization and blow-up in this system of the fully parabolic parabolic-elliptic-elliptic versions have already been proved. The purpose is to derive boundedness version.

This paper introduces a class of parabolic subgroups of real reductive groups (called “very nice”). For these parabolic subgroups we study the generalized Whittaker vectors for their degenerate principal series. It is shown that there is a holomorphic continuation of the Jacquet integrals associated with generic characters of their unipotent radicals. Also, in this context an analogue of the “m...

We define holomorphic connection on a parabolic vector bundle over a Riemann surface and prove that a parabolic vector bundle admits a holomorphic connection if and only if each direct summand of it is of parabolic degree zero. This is a generalization to the parabolic context of a well-known result of Weil which says that a holomorphic vector bundle on a Riemann surface admits a holomorphic co...

Abstract. In recent years, domain decomposition methods have attracted much attention due to their successful application to many elliptic and parabolic problems. Domain decomposition methods treat problems based on a domain substructuring, which is attractive for parallel computation, due to the independence among the subdomains. In principle, domain decomposition methods may be applied to the...