Implicit–explicit multistep methods for nonlinear parabolic equations were recently analyzed in [2, 3, 1]. In these papers the linear operator of the equation is assumed time-independent, self-adjoint and positive definite; then, the linear part is discretized implicitly and the remaining part explicitly. Here we slightly relax the hypotheses on the linear operator by allowing part of it to be ...

linear control system, 51-67Cauchy problem, 52-54controllability, 55-62Korteweg-de Vries equation, 65—67transport equation, 62-65adjoint operator, 373a d ^ y (definition), 130admissibility condition, 52, see also regularity propertyapproximate controllability, 55, 57, 61Ascoli's theorem, 152, 170attractor, 280averaging, 332-333 backstepping, 334-337, ...

planar d-bar integral equation is one of the inverse scattering solution methods for complex problems including inverse conductivity considered in applications such as electrical impedance tomography (eit). recently two different methodologies are considered for the numerical solution of d-bar integrals equation, namely product integrals and multigrid. the first one involves high computational ...

In this paper, we study ill-posedness concepts of nonlinear and linear inverse problems in a Hilbert space setting. We deene local ill-posedness of a nonlinear operator equation F(x) = y 0 in a solution point x 0 and the interplay between the nonlinear problem and its linearization using the Fr echet derivative F 0 (x 0). To nd an appropriate ill-posedness concept for 1 the linearized equation ...

We formulate the problem of solving stochastic linear operator equations in a Bayesian Ganssian process (GP) framework. The solution is obtained in the spirit of a collocation method based on noisy evaluations of the target function at randomly drawn or deliberately chosen points. Prior knowledge about the solution is encoded by the covariance kernel of the GP. As in GP regression, analytical e...

We consider the Fuchsian linear differential equation obtained (modulo a prime) for χ̃(5), the five-particle contribution to the susceptibility of the square lattice Ising model. We show that one can understand the factorization of the corresponding linear differential operator from calculations using just a single prime. A particular linear combination of χ̃(1) and χ̃(3) can be removed from χ̃(5) ...

For a general class of linear collisional kinetic models in the torus, including in particular the linearized Boltzmann equation for hard spheres, the linearized Landau equation with hard and moderately soft potentials and the semi-classical linearized fermionic and bosonic relaxation models, we prove explicit coercivity estimates on the associated integro-differential operator for some modifie...

In this paper, we study a linearized two-dimensional Euler equation. This equation decouples into infinitely many invariant subsystems. Each invariant subsystem is shown to be a linear Hamiltonian system of infinite dimensions. Another important invariant besides the Hamiltonian for each invariant subsystem is found and is utilized to prove an ‘‘unstable disk theorem’’ through a simple energy–C...

This paper is concerned with the solvability of some abstract differential equation of type u̇(t) + Au(t) + Bu(t) ∋ f(t), t ∈ (0, T ], u(0) = 0, where A is a linear selfadjoint operator and B is a nonlinear (possibly multi-valued) maximal monotone operator in a real Hilbert space H with the normalization 0 ∈ B(0). We use the concept of variational sum introduced by H. Attouch, J.-B. Baillon, and...