Exact controllability of  scalar conservation laws with strict convex flux

Adimurthi; Shyam Sundar Ghoshal; G. D. Veerappa Gowda

doi:10.3934/mcrf.2014.4.401

Article Contents

2014, Volume 4, Issue 4: 401-449. Doi: 10.3934/mcrf.2014.4.401

This issue Previous Article Next Article Well-posedness and asymptotic stability for the Lamé system with infinite memories in a bounded domain

Exact controllability of scalar conservation laws with strict convex flux

1.
Centre for Applicable Mathematics, Tata Institute of Fundamental Research, Post Bag No 6503, Sharadanagar, Bangalore - 560065

Received: February 2012

Revised: February 2014

Published: December 2014

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Abstract

We consider the scalar conservation law with strict convex flux in one space dimension. In this paper we study the exact controllability of entropy solution by using initial or boundary data control. Some partial results have been obtained in [5],[23]. Here we investigate the precise conditions under which, the exact controllability problem admits a solution. The basic ingredients in the proof of these results are, Lax-Oleinik [15] explicit formula and finer properties of the characteristics curves.

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Mathematics Subject Classification: Primary: 35L65, 35Q93.

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