Dissipative boundary conditions for 2 × 2 hyperbolic systems of conservation laws for entropy solutions in BV

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• 作者：Jean-Michel Coron^a ; ^{coron@ann.jussieu.fr" class="auth_mail" title="E-mail the corresponding author} ; Sylvain Ervedoza^b ; ^{sylvain.ervedoza@math.univ-toulouse.fr" class="auth_mail" title="E-mail the corresponding author} ; Shyam Sundar Ghoshal^c ; ^{shyam.ghoshal@gssi.infn.it" class="auth_mail" title="E-mail the corresponding author} ; Olivier Glass^d ; ^{glass@ceremade.dauphine.fr" class="auth_mail" title="E-mail the corresponding author} ; Vincent Perrollaz^e ; ^{vincent.perrollaz@lmpt.univ-tours.fr" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 January 2017
• 年：2017
• 卷：262
• 期：1
• 页码：1-30
• 全文大小：446 K

文摘

In this article, we investigate the BV stability of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039616302832&_mathId=si1.gif&_user=111111111&_pii=S0022039616302832&_rdoc=1&_issn=00220396&md5=f31711bc26a01af4b7c8025ee123e06d" title="Click to view the MathML source">2×2class="mathContainer hidden">class="mathCode">$2\times 2$ hyperbolic systems of conservation laws with strictly positive velocities under dissipative boundary conditions. More precisely, we derive sufficient conditions guaranteeing the exponential stability of the system under consideration for entropy solutions in BV. Our proof is based on a front tracking algorithm used to construct approximate piecewise constants solutions whose BV norms are controlled through a Lyapunov functional. This Lyapunov functional is inspired by the one proposed in J. Glimm's seminal work [16], modified with some suitable weights in the spirit of the previous works  and .