Well-posedness of two pseudo-parabolic problems for electrical\n conduction in heterogeneous media

2020/02/12 by Micòl Amar, Daniele Andreucci, Amar, Micol +5
Computer Science · Mathematics · #35A01 #35K70 #35M33 #58J05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2002.04935

openalex publication_date 2020/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a well-posedness result for two pseudo-parabolic problems, which can\nbe seen as two models for the same electrical conduction phenomenon in\nheterogeneous media, neglecting the magnetic field. One of the problems is the\nconcentration limit of the other one, when the thickness of the dielectric\ninclusions goes to zero. The concentrated problem involves a transmission\ncondition through interfaces, which is mediated by a suitable Laplace-Beltrami\ntype equation.\n

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