Renormalized entropy solutions to the Cauchy problem for a quasilinear first order equation

DOI10.1007/s10958-010-0186-5zbMath1222.35061OpenAlexW1973923289MaRDI QIDQ549419

P. V. Lysuho, Evgeny Yu. Panov

Publication date: 18 July 2011

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-010-0186-5

zbMATH Keywords

measurable initial functionrenormalized and generalized entropy solutions

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30) Initial value problems for nonlinear first-order PDEs (35F25) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Comparison principles in context of PDEs (35B51)

Related Items

On the decay property for periodic renormalized solutions to scalar conservation laws ⋮ Renormalized entropy solutions to the Cauchy problem for first order quasilinear conservation laws in the class of periodic functions ⋮ On the Cauchy problem for scalar conservation laws in the class of Besicovitch almost periodic functions: Global well-posedness and decay property

Cites Work

• Ordinary differential equations, transport theory and Sobolev spaces
• Example of nonuniqueness of entropy solutions in the class of locally bounded functions.
• Conservation laws with continuous flux functions
• Renormalised solutions of nonlinear parabolic problems with L¹ data: existence and uniqueness
• FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES
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