We consider the Cauchy problem for a scalar conservation law in one space dimension {ut + f(u)x = 0 u(t = 0) = ũ with f ∈ C2 (ℝ, ℝ), u ∈ BV (ℝ), u(t,x): ℝ+ × ℝ → ℝ. We introduce, in this simple setting, a new Glimm-type interaction potential: the time marginal of the entropy dissipation measure of a uniformly convex entropy. We show that the Glimm estimates hold for this functional.
AN ENTROPY BASED GLIMM-TYPE FUNCTIONAL
CARAVENNA, LAURA
2008
Abstract
We consider the Cauchy problem for a scalar conservation law in one space dimension {ut + f(u)x = 0 u(t = 0) = ũ with f ∈ C2 (ℝ, ℝ), u ∈ BV (ℝ), u(t,x): ℝ+ × ℝ → ℝ. We introduce, in this simple setting, a new Glimm-type interaction potential: the time marginal of the entropy dissipation measure of a uniformly convex entropy. We show that the Glimm estimates hold for this functional.
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