Related papers: Approximating semigroups by using pseudospectra
We propose a new approach to the study of (nonlinear) growth and instability for semilinear evolution equations with compact nonlinearities. We show, in particular, that compact nonlinear perturbations of a linear evolution equation can be…
We provide the spectral expansion in a weighted Hilbert space of a substantial class of invariant non-self-adjoint and non-local Markov operators which appear in limit theorems for positive-valued Markov processes. We show that this class…
The paper examines the existence of pseudo almost periodic solutions to some classes of partial hyperbolic evolution equations. Namely, sufficient conditions for the existence and uniqueness of pseudo almost periodic solutions to those…
In this paper, we investigate condition numbers of eigenvalue problems of matrix polynomials with nonsingular leading coefficients, generalizing classical results of matrix perturbation theory. We provide a relation between the condition…
Strong convergence rates for time-discrete numerical approximations of semilinear stochastic evolution equations (SEEs) with smooth and regular nonlinearities are well understood in the literature. Weak convergence rates for time-discrete…
The Computation of discrete Contractive semigroups becomes necessary when we deal with several types of evolution equations in Discretizable Hilbert spaces, in this work we study some properties of the discrete forms of the contractive…
Conditionspectrum measures the computational stability of solving a linear system. In this paper, ten theorems involving {\epsilon}-conditionspectrum are presented. All these theorems generalize a well known eigenvalue theorem and…
We apply polynomial approximation methods -- known in the numerical PDEs context as spectral methods -- to approximate the vector-valued function that satisfies a linear system of equations where the matrix and the right hand side depend on…
We investigate slowly converging solutions for non-linear evolution equations of elliptic or parabolic type. These equations arise from the study of isolated singularities in geometric variational problems. Slowly converging solutions have…
We introduce an alternative to the method of matched asymptotic expansions. In the "traditional" implementation, approximate solutions, valid in different (but overlapping) regions are matched by using "intermediate" variables. Here we…
We prove the existence of solutions for an evolution quasi-variational inequality with a first order quasilinear operator and a variable convex set, which is characterized by a constraint on the absolute value of the gradient that depends…
A trade-off between speed and information controls our understanding of astronomical objects. Fast-to-acquire photometric observations provide global properties, while costly and time-consuming spectroscopic measurements enable a better…
We present a novel numerical solver for the systems of coupled non-linear elliptical differential equations. The solver partitions the computational domain into a set of rectangular pseudo-spectral collocation subdomains and is especially…
Current spectral simulations of Einstein's equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudo-spectral evolutions of second order…
We improve on the Thomas-Fermi approximation for the single-particle density of fermions by introducing inhomogeneity corrections. Rather than invoking a gradient expansion, we relate the density to the unitary evolution operator for the…
We study a nonlinear pseudodifferential equation describing the dynamics of dislocations. The long time asymptotics of solutions is described by the self-similar profiles.
We investigate depoissonization, the problem of recovering asymptotics of sequence coefficients from their exponential generating function. Classical approaches rely on complex-analytic growth conditions, but here we develop real-variable…
The theory of degenerate parabolic equations of the forms \[ u_t=(\Phi(u_x))_{x} \quad {\rm and} \quad v_{t}=(\Phi(v))_{xx} \] is used to analyze the process of contour enhancement in image processing, based on the evolution model of…
The short-time and global behaviour are studied for autonomous linear evolution equations defined by generators of uniformly bounded holomorphic semigroups in a Hilbert space. A general criterion for log-convexity in time of the norm of the…
This paper discusses the spectral collocation method for numerically solving nonlocal problems: one dimensional space fractional advection-diffusion equation; and two dimensional linear/nonlinear space fractional advection-diffusion…