Locally Bounded Generalized Entropy Solutions to the Cauchy Problem for a~First-Order Quasilinear Equation
Informatics and Automation, Differential equations and dynamical systems, Tome 236 (2002), pp. 120-133
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Generalized entropy solutions for a first-order quasilinear partial differential equation are studied. It is shown that the Cauchy problem for this equation is ill-posed in the class of locally bounded functions. The examples of nonexistence and nonuniqueness of solutions are constructed. Moreover, a uniqueness theorem, which holds for solutions integrable with respect to the spatial variable, is proved.
@article{TRSPY_2002_236_a12,
author = {A. Yu. Goritskii and E. Yu. Panov},
title = {Locally {Bounded} {Generalized} {Entropy} {Solutions} to the {Cauchy} {Problem} for {a~First-Order} {Quasilinear} {Equation}},
journal = {Informatics and Automation},
pages = {120--133},
publisher = {mathdoc},
volume = {236},
year = {2002},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TRSPY_2002_236_a12/}
}
TY - JOUR AU - A. Yu. Goritskii AU - E. Yu. Panov TI - Locally Bounded Generalized Entropy Solutions to the Cauchy Problem for a~First-Order Quasilinear Equation JO - Informatics and Automation PY - 2002 SP - 120 EP - 133 VL - 236 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TRSPY_2002_236_a12/ LA - ru ID - TRSPY_2002_236_a12 ER -
%0 Journal Article %A A. Yu. Goritskii %A E. Yu. Panov %T Locally Bounded Generalized Entropy Solutions to the Cauchy Problem for a~First-Order Quasilinear Equation %J Informatics and Automation %D 2002 %P 120-133 %V 236 %I mathdoc %U http://geodesic.mathdoc.fr/item/TRSPY_2002_236_a12/ %G ru %F TRSPY_2002_236_a12
A. Yu. Goritskii; E. Yu. Panov. Locally Bounded Generalized Entropy Solutions to the Cauchy Problem for a~First-Order Quasilinear Equation. Informatics and Automation, Differential equations and dynamical systems, Tome 236 (2002), pp. 120-133. http://geodesic.mathdoc.fr/item/TRSPY_2002_236_a12/