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pro vyhledávání: '"Krupa, Sam G."'
Autor:
Krupa, Sam G., Székelyhidi Jr, László
We develop a general framework for studying non-uniqueness of the Riemann problem for the isentropic compressible Euler system in two spatial dimensions, and in this paper we present the most delicate result of our method: non-uniqueness of the conta
Externí odkaz:
http://arxiv.org/abs/2409.11296
Autor:
Krupa, Sam G.
In this paper, we consider finite time blowup of the $BV$-norm for exact solutions to genuinely nonlinear hyperbolic systems in one space dimension, in particular the $p$-system. We consider solutions verifying shock admissibility criteria such as th
Externí odkaz:
http://arxiv.org/abs/2403.07784
Autor:
Giesselmann, Jan, Krupa, Sam G.
In this paper, we develop reliable a posteriori error estimates for numerical approximations of scalar hyperbolic conservation laws in one space dimension. Our methods have no inherent small-data limitations and are a step towards error control of nu
Externí odkaz:
http://arxiv.org/abs/2306.06538
Autor:
Krupa, Sam G., Székelyhidi Jr, László
Publikováno v:
Adv. Math., 454:Paper No. 109856, 2024
We study the constitutive set $\mathcal{K}$ arising from a $2\times 2$ system of conservation laws in one space dimension, endowed with one entropy and entropy-flux pair. The convexity properties of the set $\mathcal{K}$ relate to the well-posedness
Externí odkaz:
http://arxiv.org/abs/2211.14239
Publikováno v:
In Advances in Mathematics October 2024 454
Publikováno v:
Arch. Ration. Mech. Anal., 246(1):299--332, 2022
Let a 1-d system of hyperbolic conservation laws, with two unknowns, be endowed with a convex entropy. We consider the family of small $BV$ functions which are global solutions of this equation. For any small $BV$ initial data, such global solutions
Externí odkaz:
http://arxiv.org/abs/2010.04761
Autor:
Krupa, Sam G.
Publikováno v:
J. Differential Equations, 273:122--171, 2021
In this paper on hyperbolic systems of conservation laws in one space dimension, we give a complete picture of stability for all solutions to the Riemann problem which contain only extremal shocks. We study stability of the Riemann problem amongst a
Externí odkaz:
http://arxiv.org/abs/1905.04347
Autor:
Krupa, Sam G., Vasseur, Alexis F.
Publikováno v:
SIAM J. Math. Anal., 52(3), 2491-2530, 2020
In this paper, we show uniqueness and stability for the piecewise-smooth solutions to the Burgers--Hilbert equation constructed in Bressan and Zhang [Commun. Math. Sci., 15(1):165--184, 2017]. The Burgers--Hilbert equation is $u_t+(\frac{u^2}{2})_x=\
Externí odkaz:
http://arxiv.org/abs/1904.09468
Autor:
Krupa, Sam G.
Publikováno v:
Commun. Math. Sci., 18(6):1493-1537, 2020
We show uniqueness and stability in $L^2$ and for all time for piecewise-smooth solutions to hyperbolic balance laws. We have in mind applications to gas dynamics, the isentropic Euler system and the full Euler system for a polytropic gas in particul
Externí odkaz:
http://arxiv.org/abs/1904.09475
Autor:
Krupa, Sam G., Vasseur, Alexis F.
Publikováno v:
Journal of Hyperbolic Differential Equations, 16(01):157--191, 2019
For hyperbolic systems of conservation laws, uniqueness of solutions is still largely open. We aim to expand the theory of uniqueness for systems of conservation laws. One difficulty is that many systems have only one entropy. This contrasts with sca
Externí odkaz:
http://arxiv.org/abs/1709.05610