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PDE problems with concentrating terms near the boundary

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Jiménez Casas, A. and Rodríguez Bernal, Aníbal (2020) PDE problems with concentrating terms near the boundary. Communications on pure and applied mathematics, 19 (4). pp. 2147-2195. ISSN 0010-3640

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Official URL: https://doi.org/doi:10.3934/cpaa.2020095



Abstract

In this paper we study several PDE problems where certain linear or nonlinear termsin the equation concentrate in the domain, typically (but not exclusively) near the boundary. We analyze some linear and nonlinear elliptic models, linear and nonlinear parabolic ones as well as some damped wave equations. We show that in all these singularly perturbed problems, the concentrating terms give rise in the limit to a modification in the original boundary condition of the problem. Hence we describe in each case which is
the singular limit problem and analyze the convergence of solutions.


Item Type:Article
Uncontrolled Keywords:Concentrating integrals; Singular perturbations; Boundary potentials; Convergence of solutions
Subjects:Sciences > Mathematics > Differential equations
ID Code:75949
Deposited On:14 Dec 2022 15:56
Last Modified:15 Dec 2022 09:05

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