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Quadratic interaction functional for general systems of conservation laws

Show simple item record Bianchini, Stefano Modena, Stefano 2014-10-13T08:12:56Z 2014-10-13T08:12:56Z 2014
dc.description.abstract For the Glimm scheme approximation u" to the solution of the system of conservation laws in one space dimension ut + f(u)x = 0; u(0; x) = u0(x) 2 Rn; with initial data u0 with small total variation, we prove a quadratic (w.r.t. Tot.Var.(u0)) interaction estimate, which has been used in the literature for stability and convergence results. No assumptions on the structure of the ux f are made (apart smoothness), and this estimate is the natural extension of the Glimm type interaction estimate for genuinely nonlinear systems. More precisely we obtain the following results: a new analysis of the interaction estimates of simple waves; a Lagrangian representation of the derivative of the solution, i.e. a map x(t;w) which follows the trajectory of each wave w from its creation to its cancellation; the introduction of the characteristic interval and partition for couples of waves, representing the common history of the two waves; a new functional Q controlling the variation in speed of the waves w.r.t. time. This last functional is the natural extension of the Glimm functional for genuinely nonlinear systems. The main result is that the distribution Dttx(t;w) is a measure with total mass O(1)Tot.Var.(u0)2. en_US
dc.language.iso en en_US
dc.publisher SISSA en_US
dc.relation.ispartofseries SISSA;51/2014/MATE
dc.subject Conservation laws en_US
dc.subject Interaction functionals en_US
dc.title Quadratic interaction functional for general systems of conservation laws en_US
dc.type Preprint en_US

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