In this work we estimate rates of the linear transient growth of the perturbations of cellular flames governed by the Sivashinsky equation. The possibility and significance of such a growth was indicated earlier in both computational and analytical investigations. Numerical investigation of the norm of the resolvent of the linear operator associated with the Sivashinsky equation linearized in a...

In this paper we study the operator inequality φ(X) ≤ X and the operator equation φ(X) = X, where φ is a w∗-continuous positive (resp. completely positive) linear map on B(H). We show that their solutions are in one-to-one correspondence with a class of Poisson transforms on Cuntz-Toeplitz C∗-algebras, if φ is completely positive. Canonical decompositions, ergodic type theorems, and lifting the...

A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (2D) skin tissues. In the numerical scheme, the nonlinearity caused by linear and exponential relationships of temperature-dependent blood perfusion...

We give an example of a linear, time-dependent, Schrödinger operator with optimal growth Sobolev norms. The construction is explicit, and relies on comprehensive study the linear Lowest Landau Level equation time-dependent potential.

This article shows how a (linear) scale-space representation can be de ned for discrete signals of arbitrary dimension. The treatment is based upon the assumptions that (i) the scale-space representation should be de ned by convolving the original signal with a one-parameter family of symmetric smoothing kernels possessing a semi-group property, and (ii) local extrema must not be enhanced when ...

We derive the hydrodynamic limit of a kinetic equation where interactions in velocity are modelled by linear operator (Fokker-Planck or Linear Boltzmann) and force Vlasov term is stochastic process with high amplitude short-range correlation. In scales regime we consider, scalar second-order partial differential equation. Compared to deterministic case, also observe phenomenon enhanced diffusion.

Motivated by boundary problems for linear differential equations, we define an abstract boundary problem as a pair consisting of a surjective linear map (“differential operator”) and an orthogonally closed subspace of the dual space (“boundary conditions”). Defining the composition of boundary problems corresponding to their Green’s operators in reverse order, we characterize and construct all ...

We start with a discussion of coupled algebraic Riccati equations arising in the study of linear-quadratic optimal control problem for Markov jump linear systems. Under suitable assumptions, this system of equations has a unique positive semidefinite solution, which is the solution of practical interest. The coupled equations can be rewritten as a single linearly perturbed matrix Riccati equati...

We are interested in the feedback stabilization of a fluid flow over a flat plate, around a stationary solution, in the presence of perturbations. More precisely, we want to stabilize the laminarto-turbulent transition location of a fluid flow over a flat plate. For that we study the Algebraic Riccati Equation (A.R.E.) of a control problem in which the state equation is a doubly degenerate line...