Stability estimates for the inverse boundary value problem by partial Cauchy data

We study the inverse conductivity problem with partial data in dimension n ≥ 3. We derive stability estimates for this inverse problem if the conductivity has regularity for 0 < σ < 1. Copyright © 2014 John Wiley & Sons, Ltd.     

An application of interactive multi-criteria optimization to air pollution control

In this paper a problem of air pollution control is studied, posing it as a multi-objective control problem of partial differential equations. The original problem, dealing with the optimal management of a set of industrial plants inside a populated area, is formulated by means of the diffusion transport equation, including a linear reaction term and source terms modelled by Dirac deltas. Introducing adjoint state techniques, the problem transforms into a problem of multi-objective optimization in Banach spaces, where the large number of objective functions discourages the complete search of its Pareto front. Therefore, in order to solve the problem, two interactive methods of multi-objective programming are proposed: the VIA and the STEM algorithms. Finally, the paper illustrates how to combine both algorithms to solve in a more effective way a realistic problem posed in the Metropolitan Area of Guadalajara (Mexico).     

Chemometrics‐enhanced laser‐induced thermal emission detection of PETN and other explosives on various substrates

Infrared emissions (IREs) of samples of pentaerythritol tetranitrate (PETN) deposited as contamination residues on various substrates were measured to generate models for the detection and discrimination of the important nitrate ester from the emissions of the substrates. Mid‐infrared emissions were generated by heating the samples remotely using laser‐induced thermal emission (LITE). Chemometrics multivariate analysis techniques such as principal component analysis (PCA), soft independent modeling by class analogy (SIMCA), partial least squares‐discriminant analysis (PLS‐DA), support vector machines (SVMs), and neural network (NN) were employed to generate the models for the classification and discrimination of PETN IREs from substrate thermal emissions. PCA exhibited less variability for the LITE spectra of PETN/substrates. SIMCA was able to predict only 44.7% of all samples, while SVM proved to be the most effective statistical analysis routine, with a discrimination performance of 95%. PLS‐DA and NN achieved prediction accuracies of 94% and 88%, respectively. High sensitivity and specificity values were achieved for five of the seven substrates investigated. Copyright © 2015 John Wiley & Sons, Ltd.     

A control problem for clamped extensible beams

An optimal control problem for a nonlinear partial integro-differential equation is presented. Existence of an optimal control is obtained, and a minimum principle is proved     

Singular evolution integro-differential equations with kernels defined on bounded intervals

We study linear singular first-order integro-differential Cauchy problems in Banach spaces. The adjective “singular” means here that the integro-differential equation is not in normal form neither can it be reduced to such a form. We generalize some existence and uniqueness theorems proved in [5] Favini, A, Lorenzi, A and Tanabe, H. 2002. Singular integro-differential equations of parabolic type. Advances in Differential Equations, 7: 769–798.  [Google Scholar] for kernels defined on the entire half-line R ₊ to the case of kernels defined on bounded intervals removing the strict assumption that the kernel should be Laplace-transformable.

Particular attention is paid to single out the optimal regularity properties of solutions as well as to point out several explicit applications relative to singular partial integro-differential equations of parabolic and hyperbolic type.     

一类再生Hilbert空间上偏微分算子的有界性(英文)

研究了一类再生Hilbert空间上偏微分算子的有界性,得到了偏微分算子有界的一个充分必要条件,推广了文献[1]中的结果.     

SPDEs driven by space-time white noise in high dimensions: absolute continuity of the law and convergence of solutions

In this paper, we consider stochastic partial differential equations driven by space-time white noise in high dimensions. We prove, under reasonable conditions, that the law of the solution admits a density with respect to Lebesgue measure. The stability of the equation, as the higher order differential operator tends to zero, is also studied in the paper.