JournalsaihpcVol. 34, No. 1pp. 221–248

The obstacle-mass constraint problem for hyperbolic conservation laws. Solvability

  • Paulo Amorim

    Instituto de Matemática, Universidade Federal do Rio de Janeiro, Av. Athos da Silveira Ramos 149, Centro de Tecnologia – Bloco C, Cidade Universitária – Ilha do Fundão, Caixa Postal 68530, 21941-909 Rio de Janeiro, RJ, Brazil

  • Wladimir Neves

    Instituto de Matemática, Universidade Federal do Rio de Janeiro, Av. Athos da Silveira Ramos 149, Centro de Tecnologia – Bloco C, Cidade Universitária – Ilha do Fundão, Caixa Postal 68530, 21941-909 Rio de Janeiro, RJ, Brazil

  • José Francisco Rodrigues

    CMAF+IO, F_Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal
The obstacle-mass constraint problem for hyperbolic conservation laws. Solvability cover
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Abstract

In this work we introduce the obstacle-mass constraint problem for a multidimensional scalar hyperbolic conservation law. We prove existence of an entropy solution to this problem by a penalization/viscosity method. The mass constraint introduces a nonlocal Lagrange multiplier in the penalized equation, giving rise to a nonlocal parabolic problem. We introduce a compatibility condition relating the initial datum and the obstacle function which ensures global in time existence of solution. This is not a smoothness condition, but relates to the propagation of the support of the initial datum.

Cite this article

Paulo Amorim, Wladimir Neves, José Francisco Rodrigues, The obstacle-mass constraint problem for hyperbolic conservation laws. Solvability. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 1, pp. 221–248

DOI 10.1016/J.ANIHPC.2015.11.003