L1Solutions to First Order Hyperbolic Equations in Bounded Domains

DOI10.1081/PDE-120019387zbMath1027.35066OpenAlexW2063194858MaRDI QIDQ4805328

Alessio Porretta, Julien Vovelle

Publication date: 12 May 2003

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/pde-120019387

zbMATH Keywords

initial boundary value problemrenormalized entropy solutionsfirst order quasilinear equations

Mathematics Subject Classification ID

Related Items (11)

Scalar conservation laws: initial and boundary value problems revisited and saturated solutions ⋮ Renormalized entropy solutions of stochastic scalar conservation laws with boundary condition ⋮ Heterogeneous stochastic scalar conservation laws with non-homogeneous Dirichlet boundary conditions ⋮ Lack of controllability of the viscous Burgers equation. I: the \(\mathrm{L}^{\infty}\) setting ⋮ Large deviation principles for first-order scalar conservation laws with stochastic forcing ⋮ Ergodicity for stochastic conservation laws with multiplicative noise ⋮ A kinetic approach in nonlinear parabolic problems with \(L^1\)-data ⋮ Scalar conservation laws with general boundary condition and continuous flux function ⋮ Quasilinear viscous approximations to scalar conservation laws ⋮ Well-posedness of general boundary-value problems for scalar conservation laws ⋮ Explicit formulation for the Dirichlet problem for parabolic-hyperbolic conservation laws

Cites Work

• Unnamed Item
• Boundary conditions for scalar conservation laws from a kinetic point of view
• Convergence of finite volume monotone schemes for scalar conservation laws on bounded domains
• The semigroup approach to first order quasilinear equations in several space variables
• First order quasilinear equations with boundary conditions
• Scalar non-linear conservation laws with integrable boundary data
• Explicit formula for scalar non‐linear conservation laws with boundary condition
• Dirichlet problem for a nonlinear conservation law

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