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CRITICAL THRESHOLDS IN A CONVOLUTION MODEL FOR NONLINEAR CONSERVATION LAWS

dc.contributor.authorLIU, HAILIANG
dc.contributor.authorTADMOR, EITAN
dc.date.accessioned2008-11-03T18:48:18Z
dc.date.available2008-11-03T18:48:18Z
dc.date.issued2001
dc.identifier.citationH. Liu & E. Tadmor (2001). Critical thresholds in a convolution model for nonlinear conservation laws. SIAM Journal on Mathematical Analysis 33 (2001), 930-945.en
dc.identifier.urihttp://hdl.handle.net/1903/8657
dc.description.abstractIn this work we consider a convolution model for nonlinear conservation laws.Due to the delicate balance between the nonlinear convection and the nonlocal forcing, this model allows for narrower shock layers than those in the viscous Burgers’ equation and yet exhibits the conditional finite time breakdown as in the damped Burgers’ equation.W e show the critical threshold phenomenon by presenting a lower threshold for the breakdown of the solutions and an upper threshold for the global existence of the smooth solution.The threshold condition depends only on the relative size of the minimum slope of the initial velocity and its maximal variation.W e show the exact blow-up rate when the slope of the initial profile is below the lower threshold.W e further prove the L1 stability of the smooth shock profile, provided the slope of the initial profile is above the critical threshold.en
dc.format.extent171811 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoen_USen
dc.publisherCopyright: Society for Industrial and Applied Mathematicsen
dc.subjectwave breakdownen
dc.subjectcritical thresholden
dc.subjectshock profileen
dc.subjectstabilityen
dc.titleCRITICAL THRESHOLDS IN A CONVOLUTION MODEL FOR NONLINEAR CONSERVATION LAWSen
dc.typeArticleen
dc.relation.isAvailableAtCollege of Computer, Mathematical & Physical Sciencesen_us
dc.relation.isAvailableAtMathematicsen_us
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_us
dc.relation.isAvailableAtUniversity of Maryland (College Park, MD)en_us


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