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TitleSolutions for linear conservation laws with gradient constraint
Author(s)Rodrigues, José Francisco
Santos, Lisa
KeywordsLinear conservation laws
Gradient constraints
Transport equation
Unilateral constraint
First order variational inequalities
Issue date2015
PublisherEuropean Mathematical Society Publishing House
JournalPortugaliae Mathematica
Abstract(s)We consider variational inequality solutions with prescribed gradient constraints for first order linear boundary value problems. For operators with coefficients only in L^2, we show the existence and uniqueness of the solution by using a combination of parabolic regularization with a penalization in the nonlinear diffusion coefficient. We also prove the continuous dependence of the solution with respect to the data, as well as, in a coercive case, the asymptotic stabilization as time t tends to infinity towards the stationary solution. In particular situation, motivated by the transported sandpile problem, we give sufficient conditions for the equivalence of the first order problem with gradient constraint with a two obstacles problem, the obstacles being the signed distances to the boundary. This equivalence, in special conditions, illustrates also the possible stabilization of the solution in finite time.
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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