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).
Results in Mathematics – Springer Journals
Published: Mar 23, 2017
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