Lions Regularization of the Telegraph System with Nonlinear Boundary Conditions

Lions Regularization of the Telegraph System with Nonlinear Boundary Conditions The purpose of this paper is to study a Lions type regularization of the telegraph system with nonlinear boundary conditions. An asymptotic expansion of order zero for the solution of this regularization is established, including some boundary layer corrections. Specifically, under some appropriate smoothness and compatibility conditions on the data an estimate for the remainder term of the expansion is derived with respect to the $$C([0,T];L^2(0,1)^2)$$ C ( [ 0 , T ] ; L 2 ( 0 , 1 ) 2 ) norm. Our main theorem generalizes a result regarding the particular case of homogeneous linear boundary conditions reported by Apreutesei and Djafari Rouhani (Nonlinear Anal 35:3049–3061, 2010). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Results in Mathematics Springer Journals

Lions Regularization of the Telegraph System with Nonlinear Boundary Conditions

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Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing
Subject
Mathematics; Mathematics, general
ISSN
1422-6383
eISSN
1420-9012
D.O.I.
10.1007/s00025-017-0670-z
Publisher site
See Article on Publisher Site

Abstract

The purpose of this paper is to study a Lions type regularization of the telegraph system with nonlinear boundary conditions. An asymptotic expansion of order zero for the solution of this regularization is established, including some boundary layer corrections. Specifically, under some appropriate smoothness and compatibility conditions on the data an estimate for the remainder term of the expansion is derived with respect to the $$C([0,T];L^2(0,1)^2)$$ C ( [ 0 , T ] ; L 2 ( 0 , 1 ) 2 ) norm. Our main theorem generalizes a result regarding the particular case of homogeneous linear boundary conditions reported by Apreutesei and Djafari Rouhani (Nonlinear Anal 35:3049–3061, 2010).

Journal

Results in MathematicsSpringer Journals

Published: Mar 23, 2017

References

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