Search results for "Nonlinear nonautonomous transmission problem"

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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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