La méthode des gradients conjugents pour les équations non linéaires dans l'espace de Banach
In this paper Lambert multipliers acting between spaces are characterized by using some properties of conditional expectation operator. Also, Fredholmness of corresponding bounded operators is investigated.
The time-ordered exponential of a time-dependent matrix is defined as the function of that solves the first-order system of coupled linear differential equations with non-constant coefficients encoded in . The authors have recently proposed the first Lanczos-like algorithm capable of evaluating this function. This algorithm relies on inverses of time-dependent functions with respect to a non-commutative convolution-like product, denoted by . Yet, the existence of such inverses, crucial to...
We start with a general time-homogeneous scalar diffusion whose state space is an interval I ⊆ ℝ. If it is started at x ∈ I, then we consider the problem of imposing upper and/or lower boundary conditions at two points a,b ∈ I, where a < x < b. Using a simple integral identity, we derive general expressions for the Laplace transform of the transition density of the process, if killing or reflecting boundaries are specified. We also obtain a number of useful expressions for the Laplace transforms...
We study the large time behaviour of the solutions of a nonlocal regularisation of a scalar conservation law. This regularisation is given by a fractional derivative of order , with , which is a Riesz-Feller operator. The nonlinear flux is given by the locally Lipschitz function for . We show that in the sub-critical case, , the large time behaviour is governed by the unique entropy solution of the scalar conservation law. Our proof adapts the proofs of the analogous results for the local...