On the conditions for the existence of a piecewise smooth solution of the Riemann problem for one class of conservation laws

被引：0

作者：

Aybosinova, Gulmira M. ^{[1
]}

Palin, Vladimir Vladimirovich ^{[1
]}

机构：

[1] MV Lomonosov Moscow State Univ, Fac Mech & Math, Moscow, Russia

来源：

APPLICABLE ANALYSIS | 2025年

关键词：

Conservation laws; strongly discontinuous flux function; Riemann problem; geometric solution; GEOMETRIC SOLUTIONS; DISCONTINUOUS FLUX; DIFFERENCE SCHEME; CONVERGENCE; UNIQUENESS;

D O I：

10.1080/00036811.2025.2473498

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the Riemann problem for a class of conservation laws with a strongly discontinuous (in a spatial variable) flux function. Using the method of the geometric solutions, we obtain the sufficient condition for the existence of a piecewise smooth solution and describe a constructive method to obtain such a solution. Our work, in the part concerning the sufficient condition, can be considered as a generalization of the results obtained earlier by one of the authors. The necessary condition for the existence of a piecewise smooth solution, which does not depend on the choice of the admissibility condition, is also obtained.

引用

页数：18

共 19 条

[1]

Adimurthi, 2005, J HYPERBOL DIFFER EQ, V2, P783

[2] A Theory of L 1-Dissipative Solvers for Scalar Conservation Laws with Discontinuous Flux [J].

Andreianov, Boris ;

Hvistendahl, Kenneth Karlsen ;

Risebro, Nils Henrik .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2011, 201 (01) :27-86

[3] Uniqueness for scalar conservation laws with discontinuous flux via adapted entropies [J].

Audusse, E ;

Perthame, B .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2005, 135 :253-265

[4] Well-posedness for a class of 2 x 2 conservation laws with L-infinity data [J].

Baiti, P ;

Jenssen, HK .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1997, 140 (01) :161-185

[5]

Burger R., 2005, Trends in applications of mathematics to mechanics, Ber. Math., P75

[6] A UNIQUENESS CONDITION FOR NONLINEAR CONVECTION-DIFFUSION EQUATIONS WITH DISCONTINUOUS COEFFICIENTS [J].

Diehl, Stefan .

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2009, 6 (01) :127-159

[7]

Filippov A.F., 2007, Introduction to the theory of differential equations

[8]

Garavello M, 2007, NETW HETEROG MEDIA, V2, P159

[9] VANISHING VISCOSITY AND BACKWARD EULER APPROXIMATIONS FOR CONSERVATION LAWS WITH DISCONTINUOUS FLUX [J].

Guerra, Graziano ;

Shen, Wen .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2019, 51 (04) :3112-3144

[10] NONLINEAR RESONANCE IN SYSTEMS OF CONSERVATION-LAWS [J].

ISAACSON, E ;

TEMPLE, B .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1992, 52 (05) :1260-1278

← 1 2 →