Quadratic Interaction Functional for General Systems of Conservation Laws
نویسندگان
چکیده
منابع مشابه
Quadratic Interaction Functional for Systems of Conservation Laws: a Case Study
We prove a quadratic interaction estimate for wavefront approximate solutions to the triangular system of conservation laws { ut + f̃(u, v)x = 0, vt − vx = 0. This quadratic estimate has been used in the literature to prove the convergence rate of the Glimm scheme [2]. Our aim is to extend the analysis, done for scalar conservation laws [7], in the presence of transversal interactions among wave...
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Let the smooth map f : Ω 7→ R define the strictly hyperbolic system of conservation laws ∂tu+ ∂xf(u) = 0 (1.1) where t > 0, x ∈ R and u ∈ Ω, with Ω ⊆ R being an open set. Most functional theoretic methods fail to tackle these equations, essentially due to the appearance of shock waves. Since 1965, the Glimm functional [13] has been a major tool in any existence proof for (1.1) and related equat...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2015
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-015-2372-2