Corpus ID: 119127031

Approximate solutions of scalar conservation laws

  title={Approximate solutions of scalar conservation laws},
  author={Misha Perepelitsa},
  journal={arXiv: Analysis of PDEs},
We study compactness properties of time-discrete and continuous time BGK-type schemes for scalar conservation laws, in which microscopic interactions occur only when the state of a system deviates significantly from an equilibrium distribution. The threshold deviation, $\epsilon,$ is a parameter of the problem. In the vanishing relaxation time limit we obtain solutions of a conservation law in which flux is pointwisely close (of order $\epsilon$) to the flux of the original equation and derive… Expand


Averaged Multivalued Solutions for Scalar Conservation Laws
A time discretization is introduced for scalar conservation laws, which consists in averaging (in an appropriate sense) the generally multivalued solution given by the classical method ofExpand
Kinetic formulation of the isentropic gas dynamics andp-systems
We consider the 2×2 hyperbolic system of isentropic gas dynamics, in both Eulerian or Lagrangian variables (also called thep-system). We show that they can be reformulated as a kinetic equation,Expand
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Regularity of the moments of the solution of a Transport Equation
Let u = u(x, v) satisfy the Transport Equation u+v·∂ xu=f, x∈RN, v∈RNwhere f belongs to some space of type Lp(dx ⊗ dμ(v)) (where μ is a positive bounded measure on RN). We study the resultingExpand
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Semigroups of Linear Operators and Applications to Partial Differential Equations
  • A. Pazy
  • Mathematics, Computer Science
  • Applied Mathematical Sciences
  • 1983
This chapter discusses generation and representation, applications to Partial Differential Equations-Nonlinear Equations, and the Inhomogeneous Equation in the Parabolic Initial Value Problem. Expand