Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/on-the-theory-of-divergence-measure-fields-and-its-applications-X2qXKJTQJt
References (60)
-
R. Natalini (1996)
Convergence to equilibrium for the relaxation approximations of conservation lawsCommunications on Pure and Applied Mathematics, 49
-
J. Málek (1996)
Weak and Measure-valued Solutions to Evolutionary PDEs -
W. Ziemer (1989)
Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation -
P. Lax, B. Wendroff (1960)
Systems of conservation lawsCommunications on Pure and Applied Mathematics, 13
-
A. Vol'pert (1967)
THE SPACES BV AND QUASILINEAR EQUATIONSMathematics of The Ussr-sbornik, 2
-
W. Ziemer (1983)
Cauchy flux and sets of finite perimeterArchive for Rational Mechanics and Analysis, 84
-
R. Diperna (1983)
Convergence of the viscosity method for isentropic gas dynamicsCommunications in Mathematical Physics, 91
-
G. Anzellotti (1983)
Pairings between measures and functions and compensated compactnessAnn. Mat. Pura Appl., 135
-
T. O’Neil (2002)
Geometric Measure Theory -
W.B. Jurkat, D.J.F. Nonnenmacher (1994)
A generalized n-dimensional Riemann integral and the divergence theorem with singularitiesActa Sci. Math. (Szeged), 59
-
J. Glimm (1965)
Solutions in the large for nonlinear hyperbolic systems of equationsCommunications on Pure and Applied Mathematics, 18
-
J. Rodrigues (1987)
Obstacle Problems in Mathematical Physics -
L. Schwartz (1966)
Théorie des distributions -
D. Nonnenmacher (1995)
Sets of Finite Perimeter and the Gauss-Green Theorem with SingularitiesJournal of The London Mathematical Society-second Series, 52
-
T.-P. Liu (2003)
On the Vacuum State for the Isentropic Gas Dynamics Equations -
R. Diperna (1978)
Uniqueness of Solutions to Hyperbolic Conservation Laws. -
J. Cooper (1973)
SINGULAR INTEGRALS AND DIFFERENTIABILITY PROPERTIES OF FUNCTIONSBulletin of The London Mathematical Society, 5
-
David Wagner (1987)
Equivalence of the Euler and Lagrangian equations of gas dynamics for weak solutionsJournal of Differential Equations, 68
-
Gui-Qiang Chen, H. Frid (2003)
Extended Divergence-Measure Fields and the Euler Equations for Gas DynamicsCommunications in Mathematical Physics, 236
-
K. Friedrichs, P. Lax (1971)
Systems of conservation equations with a convex extension.Proceedings of the National Academy of Sciences of the United States of America, 68 8
-
V. Shapiro (1958)
The Divergence Theorem for Discontinuous Vector FieldsAnnals of Mathematics, 68
-
H. Whitney (1934)
Analytic Extensions of Differentiable Functions Defined in Closed SetsTransactions of the American Mathematical Society, 36
-
W. Pfeffer (2001)
Derivation and Integration -
A.I. Volpert (1967)
The space BV and quasilinear equationsMat. Sb. (N.S.), 73
-
C. Baiocchi, A. Capelo, Lakshmi Jayakar (1983)
Variational and quasivariational inequalities: Applications to free boundary problems -
C. Bardos, A. Leroux, J. Nédélec (1979)
First order quasilinear equations with boundary conditionsCommunications in Partial Differential Equations, 4
-
J. Harrison, A. Norton (1992)
The Gauss-Green theorem for fractal boundariesDuke Mathematical Journal, 67
-
C. Dafermos (2000)
Hyberbolic Conservation Laws in Continuum Physics -
G.-Q. Chen, H. Frid (1999)
Divergence-measure fields and conservation lawsArch. Rational Mech. Anal., 147
-
R. Bürger, H. Frid, K. Karlsen (2002)
On a Free Boundary Problem for a Strongly Degenerate Quasi-Linear Parabolic Equation with an Application to a Model of Pressure FiltrationSIAM J. Math. Anal., 34
-
L. Evans (1992)
Measure theory and fine properties of functions -
A. Vasseur (2001)
Strong Traces for Solutions of Multidimensional Scalar Conservation LawsArchive for Rational Mechanics and Analysis, 160
-
M. Katsoulakis, A. Tzavaras (1997)
Contractive relaxation systems and the scalar multidimensional conservation lawCommunications in Partial Differential Equations, 22
-
J. Glimm, P. Lax (1970)
Decay of solutions of systems of nonlinear hyperbolic conservation lawsMemoirs of the American Mathematical Society
-
D. Serre (2000)
Systems of Conservation Laws I, II -
A. Bressan (1999)
Hyperbolic Systems of Conservation LawsRevista Matematica Complutense, 12
-
A. Szepessy (1989)
An existence result for scalar conservation laws using measure valued solutions.Communications in Partial Differential Equations, 14
-
Gui-Qiang Chen, H. Frid, Yachun Li (2002)
Uniqueness and Stability of Riemann Solutions¶with Large Oscillation in Gas DynamicsCommunications in Mathematical Physics, 228
-
H. Whitney (1957)
Geometric Integration Theory -
Gui-Qiang Chen, M. Rascle (2000)
Initial Layers and Uniqueness of¶Weak Entropy Solutions to¶Hyperbolic Conservation LawsArchive for Rational Mechanics and Analysis, 153
-
E. Gagliardo (1957)
Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in $n$ variabiliRendiconti del Seminario Matematico della Università di Padova, 27
-
P. Lax (1957)
Hyperbolic systems of conservation laws IICommunications on Pure and Applied Mathematics, 10
-
S.N. Kruzkov (1970)
First order quasilinear equations with several independent variablesMat. Sb. (N.S.), 81
-
K. Friedrichs, P. Lax (1986)
[71-1] Systems of conservation equations with a convex extension, Proc. Nat. Acad. Sci. USA, 68 (1971), 1686–1688 -
(1991)
Mixed and Hydrid Finite Element Methods -
P. Lax (1971)
Shock Waves and Entropy -
J. Harrison (1993)
Stokes' theorem for nonsmooth chainsBulletin of the American Mathematical Society, 29
-
C. Mascia, A. Porretta, A. Terracina (2002)
Nonhomogeneous Dirichlet Problems for Degenerate Parabolic-Hyperbolic EquationsArchive for Rational Mechanics and Analysis, 163
-
G. Anzellotti (1983)
Pairings between measures and bounded functions and compensated compactnessAnnali di Matematica Pura ed Applicata, 135
-
R. Diperna (1985)
Measure-valued solutions to conservation lawsArchive for Rational Mechanics and Analysis, 88
-
L.C. Evans, R.F. Gariepy (1992)
Lecture Notes on Measure Theory and Fine Properties of Functions -
S. Kružkov (1970)
FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLESMathematics of The Ussr-sbornik, 10
-
G. Bouchitté, G. Buttazzo (2001)
Characterization of optimal shapes and masses through Monge-Kantorovich equationJournal of the European Mathematical Society, 3
-
Gui-Qiang Chen, D. Levermore, Tai-Ping Liu (1994)
Hyperbolic conservation laws with stiff relaxation terms and entropyCommunications on Pure and Applied Mathematics, 47
-
W. Ziemer (1989)
Weakly differentiable functions -
Gui-Qiang Chen, H. Frid (1999)
Divergence‐Measure Fields and Hyperbolic Conservation LawsArchive for Rational Mechanics and Analysis, 147
-
P. Lax (1987)
Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves -
P.D. Lax (1971)
Contributions to Functional Analysis -
Gui-Qiang Chen, H. Frid (1999)
Vanishing Viscosity Limit for Initial-Boundary Value Problems for Conservation Laws -
P. Lions, B. Perthame, E. Tadmor (1994)
A kinetic formulation of multidimensional scalar conservation laws and related equationsJournal of the American Mathematical Society, 7
- Publisher
- Springer Journals
- Copyright
- Copyright © 2001 by Sociedade Brasileira de Matemática
- Subject
- Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
- ISSN
- 1678-7544
- eISSN
- 1678-7714
- DOI
- 10.1007/BF01233674
- Publisher site
- See Article on Publisher Site
Abstract
Divergence-measure fields are extended vector fields, including vector fields inL p and vector-valued Radon measures, whose divergences are Radon measures. Such fields arise naturally in the study of entropy solutions of nonlinear conservation laws and other areas. In this paper, a theory of divergence-measure fields is presented and analyzed, in which normal traces, a generalized Gauss-Green theorem, and product rules, among others, are established. Some applications of this theory to several nonlinear problems in conservation laws and related areas are discussed. In particular, with the aid of this theory, we prove the stability of Riemann solutions, which may contain rarefaction waves, contact discontinuities, and/or vacuum states, in the class of entropy solutions of the Euler equations for gas dynamics.
Journal
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Feb 11, 2005