We present several suucient conditions for exponential stability and di-chotomy of solutions of the evolution equation u 0 (t) = A(t)u(t) () on a Banach space X. Our main theorem says that if the operators A(t) generate analytic semigroups on X having exponential dichotomy with uniform constants and A() has a suuciently small HH older constant, then () has exponential dichotomy. We further stud...

Exponential time integrators are well-established discretization methods for semilinear systems of ordinary differential equations. These use ? ? functions, which matrix functions related to the exponential. This work introduces an algorithm speed up computation function action over vectors two-dimensional (2D) matrices expressed as a Kronecker sum. For that, we present auxiliary exponential-re...

We study the stochastic heat equation ∂tu = Lu+σ(u)Ẇ in (1+1) dimensions, where Ẇ is space-time white noise, σ : R → R is Lipschitz continuous, and L is the generator of a Lévy process. We assume that the underlying Lévy process has finite exponential moments in a neighborhood of the origin and u0 has exponential decay at ±∞. Then we prove that under natural conditions on σ: (i) The νth absolut...

The migration of melt through the mantle of the Earth is governed by a third-order nonlinear partial differential equation for the voidage or volume fraction of melt. The partial differential equation depends on the permeability of the medium which is assumed to be a function of the voidage. It is shown that the partial differential equation admits, as well as translations in time and space, ot...

in this paper we use a class of stochastic functional kolmogorov-type model with jumps to describe the evolutions of population dynamics. by constructing a special lyapunov function, we show that the stochastic functional differential equation associated with our model admits a unique global solution in the positive orthant, and, by the exponential martingale inequality with jumps, we dis...

OBJECTIVE Respiratory pressure-volume curves fitted to exponential equations have been used to assess disease severity and prognosis in spontaneously breathing patients with idiopathic pulmonary fibrosis. Sigmoidal equations have been used to fit pressure-volume curves for mechanically ventilated patients but not for idiopathic pulmonary fibrosis patients. We compared a sigmoidal model and an e...

For sufficiently small perturbations with continuous derivative, we show how to establish the optimal regularity of invariant center manifolds when the linear equation admits a nonuniform exponential trichotomy. We also consider the general case of exponential growth rates given by an arbitrary function. This includes the usual exponential behavior as a very special case. Our proof uses the fib...

A φ-exponential distribution is a generalization of an exponential distribution associated to functions φ in an appropriate class, and the space of φ-exponential distributions has a dually flat structure. We study features of the space of φexponential distributions, such as the convexity in Wasserstein geometry and the stability under an evolution equation. From this study, we provide the new c...