Search results for "Nonlinear"

Long-transient conoscopic pattern technique

1999

0038-1098; Recent results on laser induced anisotropy in terbium gallium garnet are extended to the dynamic regime. We observed that the characteristic conoscopic pattern formation time presents a quadratic dependence on the beam size. The observed pattern intensity is accounted for by a simple analytical formula. The transient refractive index change due to thermal stress in the terbium gallium garnet is determined. (C) 1999 Elsevier Science Ltd. All rights reserved.

Nonlinear Liouville Problems in a Quarter Plane

2016

We answer affirmatively the open problem proposed by Cabr\'e and Tan in their paper "Positive solutions of nonlinear problems involving the square root of the Laplacian" (see Adv. Math. {\bf 224} (2010), no. 5, 2052-2093).

Asymptotic mean value formulas for parabolic nonlinear equations

2021

In this paper we characterize viscosity solutions to nonlinear parabolic equations (including parabolic Monge–Ampère equations) by asymptotic mean value formulas. Our asymptotic mean value formulas can be interpreted from a probabilistic point of view in terms of dynamic programming principles for certain two-player, zero-sum games. peerReviewed

Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities

2022

We consider increasing stability in the inverse Schr\"{o}dinger potential problem with power type nonlinearities at a large wavenumber. Two linearization approaches, with respect to small boundary data and small potential function, are proposed and their performance on the inverse Schr\"{o}dinger potential problem is investigated. It can be observed that higher order linearization for small boundary data can provide an increasing stability for an arbitrary power type nonlinearity term if the wavenumber is chosen large. Meanwhile, linearization with respect to the potential function leads to increasing stability for a quadratic nonlinearity term, which highlights the advantage of nonlinearit…

A posteriori error estimates for variational problems in the theory of viscous fluids

2016

The papers included in the thesis are focused on functional type a posteriori error estimates for the Stokes problem, the Stokes problem with friction type boundary conditions, the Oseen problem, and the anti-plane Bingham problem. In the summary of the thesis we consider only the Oseen problem. The papers present and justify special forms of these estimates which are suitable for the approximations generated by the Uzawa algorithm. The estimates are of two main types. Estimates of the first type use exact solutions obtained on the steps of the Uzawa algorithm. They show how errors encompassed in Uzawa approximations behave and have mainly theoretical meaning. Estimates of the second type o…

Asymptotic Mean-Value Formulas for Solutions of General Second-Order Elliptic Equations

2022

Abstract We obtain asymptotic mean-value formulas for solutions of second-order elliptic equations. Our approach is very flexible and allows us to consider several families of operators obtained as an infimum, a supremum, or a combination of both infimum and supremum, of linear operators. The families of equations that we consider include well-known operators such as Pucci, Issacs, and k-Hessian operators.

Gradient nonlinear elliptic systems driven by a (p,q)-laplacian operator

2017

In this paper, using variational methods and critical point theorems, we prove the existence of multiple weak solutions for a gradient nonlinear Dirichlet elliptic system driven by a (p, q)-Laplacian operator.

Variational parabolic capacity

2015

We establish a variational parabolic capacity in a context of degenerate parabolic equations of $p$-Laplace type, and show that this capacity is equivalent to the nonlinear parabolic capacity. As an application, we estimate the capacities of several explicit sets.

FORMAZIONE DI PATTERN PER IL PROCESSO DELL'ELETTRODEPOSIZIONE IN MODELLI DI TIPO REAZIONE-DIFFUSIONE

2014

Optical Amplification in Hollow-Core Negative-Curvature Fibers Doped with Perovskite CsPbBr

2019

We report a hollow-core negative-curvature fiber (HC-NCF) optical signal amplifier fabricated by the filling of the air microchannels of the fiber with all-inorganic CsPbBr3 perovskite nanocrystals (PNCs). The optimum fabrication conditions were found to enhance the optical gain, up to +3 dB in the best device. Experimental results were approximately reproduced by a gain assisted mechanism based on the nonlinear optical properties of the PNCs, indicating that signal regeneration can be achieved under low pump powers, much below the threshold of stimulated emission. The results can pave the road for new functionalities of the HC-NCF with PNCs, such as optical amplification, nonlinear frequen…