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A CHARACTERIZATION OF THE REACHABLE PROFILES OF ENTROPY SOLUTIONS FOR THE ELEMENTARY WAVE INTERACTION PROBLEM OF CONVEX SCALAR CONSERVATION LAWS

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dc.creatorANÍBAL CORONEL PÉREZ
dc.date2025
dc.date.accessioned2025-12-15T13:18:07Z
dc.date.available2025-12-15T13:18:07Z
dc.date.issued2025
dc.description.abstractIN THIS PAPER, WE ANALYZE AND CHARACTERIZE THE SET WHICH CONSISTS OF ALL POSSIBLE PROFILES AT A FIXED TIME OF THE ENTROPY SOLUTION OF THE ELEMENTARY WAVE INTERACTION PROBLEM IN A BOUNDED DOMAIN FOR A CONVEX SCALAR CONSERVATION LAW. THE ELEMENTARY WAVE INTERACTION PROBLEM IS THE INITIAL AND BOUNDARY VALUE PROBLEM FOR A SCALAR CONSERVATION LAW, WHERE THE FLUX IS A STRICTLY CONVEX FUNCTION, AND THE INITIAL AND BOUNDARY DATA ARE CONSTANT FUNCTIONS. IN THE FIRST MAIN RESULT OF THE ARTICLE, WE STATE AND PROVE THAT IS A SUBSET OF THE SET OF PIECEWISE FUNCTIONS THAT ARE CONSTANT ON EACH SUBDOMAIN, OR THERE IS A SUBDOMAIN WHERE THE FUNCTION IS STRICTLY INCREASING. WE PROVE THE RESULT BY APPLYING THE METHOD OF CHARACTERISTICS IN THREE STEPS: THE RIEMANN PROBLEM SOLUTION, THE ENTROPY SOLUTION OF THE INTERACTION OF TWO RIEMANN PROBLEMS, AND RESTRICTION OF THE ENTROPY SOLUTION TO THE SPATIAL BOUNDED DOMAIN. MOREOVER, WE CHARACTERIZE THE STRICTLY INCREASING PART OF THE SOLUTION
dc.formatapplication/pdf
dc.identifier.doi10.3934/math.2025145
dc.identifier.issn2473-6988
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/14299
dc.language
dc.publisherAIMS MATHEMATICS
dc.relation.uri10.3934/math.2025145
dc.rightsOPEN ACCESS
dc.subjectElementary wave interaction
dc.subjectRiemann problem
dc.subjectEntropy solutions
dc.subjectReachable profiles
dc.titleA CHARACTERIZATION OF THE REACHABLE PROFILES OF ENTROPY SOLUTIONS FOR THE ELEMENTARY WAVE INTERACTION PROBLEM OF CONVEX SCALAR CONSERVATION LAWS
dc.typeARTÍCULO
dspace.entity.typePublication
oaire.fundingReferenceANID- AGENCIA NACIONAL DE INVESTIGACIÓN Y DESARROLLO (EX CONICYT)
oaire.licenseConditionCC BY 4.0
ubb.EstadoPUBLICADA
ubb.Otra ReparticionDEPARTAMENTO DE CIENCIAS BASICAS
ubb.SedeCHILLÁN
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