0000000000409906

AUTHOR

Paolo Musolino

showing 9 related works from this author

A tribute to Massimo Lanza de Cristoforis

2020

It is with great pleasure that we dedicate the special issue Functional Analytic Methods in Partial Differential Equations of Complex Variables and Elliptic Equations to the 60th birthday of Massim...

A tribute to Lanza de CristoforisNumerical AnalysisPartial differential equationApplied Mathematicsmedia_common.quotation_subject010102 general mathematicsSettore MAT/04 - Matematiche Complementari01 natural sciencesPhysics::History of PhysicsPleasure010101 applied mathematicsAlgebraComputational MathematicsH. BegehrSettore MAT/05 - Analisi MatematicaComplex variables0101 mathematicsAnalysisMathematicsmedia_common
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Moderately close Neumann inclusions for the Poisson equation

2016

We investigate the behavior of the solution of a mixed problem for the Poisson equation in a domain with two moderately close holes. If ϱ1 and ϱ2 are two positive parameters, we define a perforated domain Ω(ϱ1,ϱ2) by making two small perforations in an open set: the size of the perforations is ϱ1ϱ2, while the distance of the cavities is proportional to ϱ1. Then, if r∗ is small enough, we analyze the behavior of the solution for (ϱ1,ϱ2) close to the degenerate pair (0,r∗). Copyright © 2016 John Wiley & Sons, Ltd.

General Mathematics010102 general mathematicsMathematical analysisGeneral Engineeringmixed problem; moderately close holes; Poisson equation; real analytic continuation in Banach space; singularly perturbed perforated domain; Mathematics (all); Engineering (all)Poisson equation01 natural sciences010101 applied mathematicsmixed problemsingularly perturbed perforated domainEngineering (all)Settore MAT/05 - Analisi MatematicaMathematics (all)0101 mathematicsPoisson's equationmoderately close holesMathematicsreal analytic continuation in Banach space
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Global representation and multiscale expansion for the Dirichlet problem in a domain with a small hole close to the boundary

2019

For each pair (Formula presented.) of positive parameters, we define a perforated domain (Formula presented.) by making a small hole of size (Formula presented.) in an open regular subset (Formula presented.) of (Formula presented.) ((Formula presented.)). The hole is situated at distance (Formula presented.) from the outer boundary (Formula presented.) of the domain. Thus, when (Formula presented.) both the size of the hole and its distance from (Formula presented.) tend to zero, but the size shrinks faster than the distance. Next, we consider a Dirichlet problem for the Laplace equation in the perforated domain (Formula presented.) and we denote its solution by (Formula presented.) Our ai…

multiscale asymptotic expansionmulti-scale asymptotic expansionBoundary (topology)01 natural sciences35J25; 31B10; 45A05; 35B25; 35C20Domain (mathematical analysis)Settore MAT/05 - Analisi MatematicaSituated[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]Dirichlet problem; Laplace operator; multiscale asymptotic expansion; real analytic continuation in Banach space; singularly perturbed perforated domainSmall hole[MATH]Mathematics [math]0101 mathematicsRepresentation (mathematics)MathematicsDirichlet problemDirichlet problemApplied Mathematics010102 general mathematicsMathematical analysisA domain010101 applied mathematicssingularly perturbed perforated domainLaplace operatorLaplace operatorAnalysisreal analytic continuation in Banach space
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Multi-parameter analysis of the obstacle scattering problem

2022

Abstract We consider the acoustic field scattered by a bounded impenetrable obstacle and we study its dependence upon a certain set of parameters. As usual, the problem is modeled by an exterior Dirichlet problem for the Helmholtz equation Δu + k 2 u = 0. We show that the solution u and its far field pattern u ∞ depend real analytically on the shape of the obstacle, the wave number k, and the Dirichlet datum. We also prove a similar result for the corresponding Dirichlet-to-Neumann map.

integral equationsshape sensitivity analysisassociated exterior Dirichlet problemDirichlet-to-Neumann operatorApplied MathematicsHelmholtz equation; acoustic scattering; associated exterior Dirichlet problem; Dirichlet-to-Neumann operator; shape sensitivity analysis; perturbed domain; integral equationsacoustic scatteringComputer Science ApplicationsTheoretical Computer Scienceperturbed domainMathematics - Analysis of PDEsSettore MAT/05 - Analisi MatematicaSignal ProcessingFOS: Mathematicsacoustic scattering; associated exterior Dirichlet problem; Dirichlet-to-Neumann operator; Helmholtz equation; integral equations; perturbed domain; shape sensitivity analysisHelmholtz equation35J25 35J05 35P25 31B10 45A05Mathematical PhysicsAnalysis of PDEs (math.AP)
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Mapping properties of weakly singular periodic volume potentials in Roumieu classes

2020

The analysis of the dependence of integral operators on perturbations plays an important role in the study of inverse problems and of perturbed boundary value problems. In this paper, we focus on the mapping properties of the volume potentials with weakly singular periodic kernels. Our main result is to prove that the map which takes a density function and a periodic kernel to a (suitable restriction of the) volume potential is bilinear and continuous with values in a Roumieu class of analytic functions. This result extends to the periodic case of some previous results obtained by the authors for nonperiodic potentials, and it is motivated by the study of perturbation problems for the solut…

Integral operatorsNumerical AnalysisIntegral operators; Periodic kernels; Periodic volume potentials; Roumieu classes; Special nonlinear operatorsDifferential equationApplied Mathematics010102 general mathematicsMathematical analysisSpecial nonlinear operatorsBilinear interpolationPerturbation (astronomy)Probability density functionInverse problem01 natural sciences31B10010101 applied mathematicsSettore MAT/05 - Analisi MatematicaKernel (statistics)Boundary value problemPeriodic volume potentials0101 mathematics47H30Roumieu classesPeriodic kernelsAnalytic functionMathematics
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A Dirichlet problem for the Laplace operator in a domain with a small hole close to the boundary

2016

We study the Dirichlet problem in a domain with a small hole close to the boundary. To do so, for each pair $\boldsymbol\varepsilon = (\varepsilon_1, \varepsilon_2 )$ of positive parameters, we consider a perforated domain $\Omega_{\boldsymbol\varepsilon}$ obtained by making a small hole of size $\varepsilon_1 \varepsilon_2 $ in an open regular subset $\Omega$ of $\mathbb{R}^n$ at distance $\varepsilon_1$ from the boundary $\partial\Omega$. As $\varepsilon_1 \to 0$, the perforation shrinks to a point and, at the same time, approaches the boundary. When $\boldsymbol\varepsilon \to (0,0)$, the size of the hole shrinks at a faster rate than its approach to the boundary. We denote by $u_{\bolds…

Asymptotic analysisGeneral MathematicsBoundary (topology)Asymptotic expansion01 natural sciences35J25; 31B10; 45A05; 35B25; 35C20Mathematics - Analysis of PDEsSettore MAT/05 - Analisi MatematicaFOS: Mathematics[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]Mathematics (all)Mathematics - Numerical Analysis0101 mathematicsMathematicsDirichlet problemLaplace's equationDirichlet problemAnalytic continuationApplied Mathematics010102 general mathematicsMathematical analysisHigh Energy Physics::PhenomenologyReal analytic continuation in Banach spaceNumerical Analysis (math.NA)Physics::Classical Physics010101 applied mathematicsasymptotic analysisLaplace operatorPhysics::Space PhysicsAsymptotic expansion; Dirichlet problem; Laplace operator; Real analytic continuation in Banach space; Singularly perturbed perforated domain; Mathematics (all); Applied MathematicsAsymptotic expansionLaplace operator[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]Singularly perturbed perforated domainAnalytic functionAnalysis of PDEs (math.AP)Asymptotic expansion; Dirichlet problem; Laplace operator; Real analytic continuation in Banach space; Singularly perturbed perforated domain;
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Local uniqueness of the solutions for a singularly perturbed nonlinear nonautonomous transmission problem

2020

Abstract We consider the Laplace equation in a domain of R n , n ≥ 3 , with a small inclusion of size ϵ . On the boundary of the inclusion we define a nonlinear nonautonomous transmission condition. For ϵ small enough one can prove that the problem has solutions. In this paper, we study the local uniqueness of such solutions.

Local uniqueness of the solutionsLaplace's equation020502 materialsApplied MathematicsNonlinear nonautonomous transmission problem010102 general mathematicsMathematical analysisA domainBoundary (topology)02 engineering and technology01 natural sciencesNonlinear systemMathematics - Analysis of PDEs35J25 31B10 35J65 35B25 35A020205 materials engineeringTransmission (telecommunications)Settore MAT/05 - Analisi MatematicaLocal uniqueness of the solutions; Nonlinear nonautonomous transmission problem; Singularly perturbed perforated domainFOS: MathematicsUniqueness0101 mathematicsSingularly perturbed perforated domainAnalysisMathematicsAnalysis of PDEs (math.AP)
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Existence results for a nonlinear nonautonomous transmission problem via domain perturbation

2021

In this paper we study the existence and the analytic dependence upon domain perturbation of the solutions of a nonlinear nonautonomous transmission problem for the Laplace equation. The problem is defined in a pair of sets consisting of a perforated domain and an inclusion whose shape is determined by a suitable diffeomorphism $\phi$. First we analyse the case in which the inclusion is a fixed domain. Then we will perturb the inclusion and study the arising boundary value problem and the dependence of a specific family of solutions upon the perturbation parameter $\phi$.

PhysicsGeneral MathematicsMathematical analysisNonlinear nonautonomous transmission problemPerturbation (astronomy)special nonlinear operatorsLaplace equationDomain (software engineering)Nonlinear systemTransmission (telecommunications)Domain perturbationSettore MAT/05 - Analisi Matematicareal analyticitydomain perturbation; Laplace equation; Nonlinear nonautonomous transmission problem; real analyticity; special nonlinear operators
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Series expansion for the effective conductivity of a periodic dilute composite with thermal resistance at the two-phase interface

2019

We study the asymptotic behavior of the effective thermal conductivity of a periodic two-phase dilute composite obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material, each of them of size proportional to a positive parameter ?. We assume that the normal component of the heat flux is continuous at the two-phase interface, while we impose that the temperature field displays a jump proportional to the normal heat flux. For ? small, we prove that the effective conductivity can be represented as a convergent power series in ? and we determine the coefficients in terms of the solutions of explicit systems of integral equations.

Materials scienceasymptotic expansionGeneral MathematicsThermal resistanceInterface (computing)Composite numberperiodic dilute compositeConductivityEffective conductivitySettore MAT/05 - Analisi MatematicaPhase (matter)Mathematics (all)non-ideal contact conditionComposite materialSeries expansionsingularly perturbed domainasymptotic expansion; Effective conductivity; non-ideal contact condition; periodic dilute composite; singularly perturbed domain; Mathematics (all)
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