# American Institute of Mathematical Sciences

April  2020, 19(4): 2147-2195. doi: 10.3934/cpaa.2020095

## PDE problems with concentrating terms near the boundary

 1 Grupo de Dinámica No Lineal, Universidad Pontificia Comillas de Madrid, C/ Alberto Aguilera 23, 28015 Madrid, Spain 2 Departamento de Análisis Matemático y Matemática Aplicada, Universidad Complutense de Madrid. 28040 Madrid, Spain 3 Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM

*Corresponding author

Dedicated to Professor Tom´as Caraballo on occasion of his Sixtieth Birthday

Received  May 2019 Revised  September 2019 Published  January 2020

Fund Project: Partially supported by Project MTM2016-75465, MINECO, Spain and FIS2016-78883-C2-2-P(AEI/FEDER, U.E.). Partially supported by Severo Ochoa project SEV-2015-0554 (MINECO).

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.

Citation: Ángela Jiménez-Casas, Aníbal Rodríguez-Bernal. PDE problems with concentrating terms near the boundary. Communications on Pure & Applied Analysis, 2020, 19 (4) : 2147-2195. doi: 10.3934/cpaa.2020095
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##### References:
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