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Mat. Sb. (N.S.), 1967, Volume 73(115), Number 2, Pages 255–302 (Mi msb4127)  

This article is cited in 148 scientific papers (total in 148 papers)

The spaces $BV$ and quasilinear equations

A. I. Vol'pert

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English version:
Mathematics of the USSR-Sbornik, 1967, 2:2, 225–267

Bibliographic databases:

UDC: 513.881+517.29+517.945.6
MSC: 35K20, 46A32, 45E05
Received: 25.10.1966

Citation: A. I. Vol'pert, “The spaces $BV$ and quasilinear equations”, Mat. Sb. (N.S.), 73(115):2 (1967), 255–302; Math. USSR-Sb., 2:2 (1967), 225–267

Citation in format AMSBIB
\by A.~I.~Vol'pert
\paper The spaces $BV$ and quasilinear equations
\jour Mat. Sb. (N.S.)
\yr 1967
\vol 73(115)
\issue 2
\pages 255--302
\jour Math. USSR-Sb.
\yr 1967
\vol 2
\issue 2
\pages 225--267

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    1. A. I. Vol'pert, S. I. Khudyaev, “Cauchy's problem for degenerate second order quasilinear parabolic equations”, Math. USSR-Sb., 7:3 (1969), 365–387  mathnet  crossref  mathscinet  zmath
    2. S. N. Kruzhkov, “First order quasilinear equations in several independent variables”, Math. USSR-Sb., 10:2 (1970), 217–243  mathnet  crossref  mathscinet  zmath
    3. Michael G. Crandall, “The semigroup approach to first order quasilinear equations in several space variables”, Isr J Math, 12:2 (1972), 108  crossref  mathscinet  zmath
    4. Mauro Fabrizio, “Soluzioni generalizzate e disuguaglianze variazionali per alcuni sistemi differenziali non lineari della fisica matematica”, Annali di Matematica, 95:1 (1973), 63  crossref  mathscinet  zmath
    5. É. B. Bykhovskii, “A global boundary-value problem for a quasilinear differential equation of first order”, Math. USSR-Izv., 8:6 (1974), 1387–1431  mathnet  crossref  mathscinet  zmath
    6. Tai-Ping Liu, “Shock waves in the nonisentropic gas flow”, Journal of Differential Equations, 22:2 (1976), 442  crossref  mathscinet  zmath
    7. Ronald J. DiPerna, “Decay of solutions of hyperbolic systems of conservation laws with a convex extension”, Arch Rational Mech Anal, 64:1 (1977), 1  crossref  mathscinet  zmath  adsnasa
    8. É. B. Bykhovskii, “A boundary value problem for a quasilinear equation of first order with arbitrary dependence of the direction of the characteristics at the boundary on the unknown function”, Math. USSR-Izv., 11:2 (1977), 397–416  mathnet  crossref  mathscinet  zmath
    9. Michael Crandall, Andrew Majda, “The method of fractional steps for conservation laws”, Numer Math, 34:3 (1980), 285  crossref  mathscinet  zmath  isi
    10. Ronald J. Diperna, “Finite difference schemes for conservation laws”, Comm Pure Appl Math, 35:3 (1982), 379  crossref  mathscinet  zmath
    11. David H. Wagner, “The Riemann Problem in Two Space Dimensions for a Single Conservation Law”, SIAM J Math Anal, 14:3 (1983), 534  crossref  mathscinet  zmath  isi
    12. R. J. DiPerna, “Convergence of approximate solutions to conservation laws”, Arch Rational Mech Anal, 82:1 (1983), 27  crossref  mathscinet  zmath  adsnasa
    13. Kuo-Shung Cheng, “Constructing solutions of a single conservation law”, Journal of Differential Equations, 49:3 (1983), 344  crossref  mathscinet  zmath
    14. Primo Brandi, Anna Salvadori, “On convergence in area in the generalized sense”, Journal of Mathematical Analysis and Applications, 92:1 (1983), 119  crossref  mathscinet  zmath
    15. Kuo-Shung Cheng, “The space BV is not enough for hyperbolic conservation laws”, Journal of Mathematical Analysis and Applications, 91:2 (1983), 559  crossref  mathscinet  zmath
    16. A. Y. Le Roux, P. Quesseveur, “Convergence of an Antidiffusion Lagrange-Euler Scheme for Quasilinear Equations”, SIAM J Numer Anal, 21:5 (1984), 985  crossref  mathscinet  zmath  isi
    17. Yann Brenier, “Averaged Multivalued Solutions for Scalar Conservation Laws”, SIAM J Numer Anal, 21:6 (1984), 1013  crossref  mathscinet  zmath  isi
    18. Jens Lorenz, “Analysis of Difference Schemes for a Stationary Shock Problem”, SIAM J Numer Anal, 21:6 (1984), 1038  crossref  mathscinet  zmath  isi
    19. Ronald J. Diperna, “Singularities and oscillations in solutions to conservation laws”, Physica D: Nonlinear Phenomena, 12:1-3 (1984), 363  crossref  mathscinet  zmath
    20. Eitan Tadmor, “Skew-selfadjoint form for systems of conservation laws”, Journal of Mathematical Analysis and Applications, 103:2 (1984), 428  crossref  mathscinet  zmath
    21. Ronald J. DiPerna, “Measure-valued solutions to conservation laws”, Arch Rational Mech Anal, 88:3 (1985), 223  crossref  mathscinet  zmath
    22. Ronald J. DiPerna, Andrew Majda, “The validity of nonlinear geometric optics for weak solutions of conservation laws”, Comm Math Phys, 98:3 (1985), 313  crossref  mathscinet  zmath
    23. Bradley J. Lucier, “On sobolev regularizations of hyperbolic conservationlaws laws”, Communications in Partial Differential Equations, 10:1 (1985), 1  crossref  mathscinet  zmath
    24. Stephen A Williams, Richard C Scalzo, “Differential games and BV functions”, Journal of Differential Equations, 59:3 (1985), 296  crossref  mathscinet  zmath
    25. Cesari L., “Nonlinear-Analysis”, Boll. Unione Mat. Italiana, 4A:2 (1985), 157–216  mathscinet  zmath  isi
    26. Kuo-Shung Cheng, “A regularity theorem for a nonconvex scalar conservation law”, Journal of Differential Equations, 61:1 (1986), 79  crossref  mathscinet
    27. Jens Lorenz, Richard Sanders, “On the Rate of Convergence of Viscosity Solutions for Boundary Value Problems”, SIAM J Math Anal, 18:2 (1987), 306  crossref  mathscinet  zmath  isi
    28. L. Cesari, P. Brandi, A. Salvadori, “Existence theorems concerning simple integrals of the calculus of variations for discontinuous solutions”, Arch Rational Mech Anal, 98:4 (1987), 307  crossref  mathscinet  zmath  adsnasa
    29. S. N. Kruzhkov, N. S. Petrosyan, “Asymptotic behaviour of the solutions of the Cauchy problem for non-linear first order equations”, Russian Math. Surveys, 42:5 (1987), 1–47  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    30. David H Wagner, “Equivalence of the Euler and Lagrangian equations of gas dynamics for weak solutions”, Journal of Differential Equations, 68:1 (1987), 118  crossref  mathscinet  zmath
    31. J.J Moreau, M Valadier, “A chain rule involving vector functions of bounded variation”, Journal of Functional Analysis, 74:2 (1987), 333  crossref  mathscinet  zmath
    32. Bradley J. Lucier, “Regularity Through Approximation for Scalar Conservation Laws”, SIAM J Math Anal, 19:4 (1988), 763  crossref  mathscinet  isi
    33. H. Holden, L. Holden, R. Høegh-Krohn, “A numerical method for first order nonlinear scalar conservation laws in one-dimension”, Computers & Mathematics with Applications, 15:6-8 (1988), 595  crossref  mathscinet  zmath
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    35. I-Liang Chern, “Stability theorem and truncation error analysis for the Glimm scheme and for a front tracking method for flows with strong discontinuities”, Comm Pure Appl Math, 42:6 (1989), 815  crossref  mathscinet  zmath
    36. Witold Kosiński, B. Brosowski, “Admissibility and uniqueness of weak solutions to hyperbolic systems of balance laws”, Math Meth Appl Sci, 11:2 (1989), 253  crossref  mathscinet  zmath  isi
    37. B. Dakoronya, “Slabaya nepreryvnost i slabaya polunepreryvnost snizu nelineinykh funktsionalov”, UMN, 44:4(268) (1989), 35–98  mathnet  mathscinet  zmath
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    39. G. Bellettini, M. Paolini, C. Verdi, “Numerical minimization of geometrical type problems related to calculus of variations”, Calcolo, 27:3-4 (1990), 251  crossref  mathscinet  zmath
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    76. Tai-Ping Liu, Tong Yang, “Well-posedness theory for hyperbolic conservation laws”, Comm Pure Appl Math, 52:12 (1999), 1553  crossref  mathscinet  zmath
    77. Bouchut François, James François, “Duality solutions for pressureless gases, monotone scalar conservation laws, and uniqueness”, Communications in Partial Differential Equations, 24:11-12 (1999), 2173  crossref  mathscinet  zmath  elib
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    81. R. Bürger, S. Evje, K.Hvistendahl Karlsen, “On Strongly Degenerate Convection–Diffusion Problems Modeling Sedimentation–Consolidation Processes”, Journal of Mathematical Analysis and Applications, 247:2 (2000), 517  crossref  mathscinet
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    124. S. Albeverio, V. G. Danilov, “Global in time solutions to Kolmogorov-Feller pseudodifferential equations with small parameter”, Russ. J. Math. Phys, 18:1 (2011), 10  crossref  mathscinet  zmath
    125. Micol Amar, Virginia De Cicco, “Relaxation of quasi-convex integrals of arbitrary order”, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 124:05 (2011), 927  crossref  mathscinet
    126. Patricio Aviles, Yoshikazu Giga, “On lower semicontinuity of a defect energy obtained by a singular limit of the Ginzburg–Landau type energy for gradient fields”, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 129:01 (2011), 1  crossref  mathscinet
    127. Lia Bronsard, Harald Garcke, Barbara Stoth, “A multi-phase Mullins–Sekerka system: matched asymptotic expansions and an implicit time discretisation for the geometric evolution problem”, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 128:03 (2011), 481  crossref  mathscinet
    128. K.T. Joseph, Manas R. Sahoo, “Some exact solutions of 3-dimensional zero-pressure gas dynamics system”, Acta Mathematica Scientia, 31:6 (2011), 2107  crossref  mathscinet  zmath
    129. Sergio Albeverio, Vladimir Danilov, “Construction of global-in-time solutions to Kolmogorov-Feller pseudodifferential equations with a small parameter using characteristics”, Math. Nachr, 2011, n/a  crossref  mathscinet  zmath
    130. C. Bahadoran, “Hydrodynamics and Hydrostatics for a Class of Asymmetric Particle Systems with Open Boundaries”, Commun. Math. Phys, 2012  crossref  mathscinet  zmath
    131. Hanchun Yang, Yanyan Zhang, “New developments of delta shock waves and its applications in systems of conservation laws”, Journal of Differential Equations, 2012  crossref  mathscinet
    132. F. James, N. Vauchelet, “Chemotaxis: from kinetic equations to aggregate dynamics”, Nonlinear Differ. Equ. Appl, 2012  crossref  mathscinet
    133. Jimmy Lamboley, Arian Novruzi, Michel Pierre, “Regularity and Singularities of Optimal Convex Shapes in the Plane”, Arch Rational Mech Anal, 2012  crossref  mathscinet
    134. Frank Morgan, Aldo Pratelli, “Existence of isoperimetric regions in
      with density”, Ann Glob Anal Geom, 2012  crossref  mathscinet
    135. NICOLAS BESSE, “GLOBAL WEAK SOLUTIONS FOR THE RELATIVISTIC WATERBAG CONTINUUM”, Math. Models Methods Appl. Sci, 22:01 (2012), 1150001  crossref  mathscinet  zmath
    136. Henrik Kalisch, Darko Mitrović, “Singular solutions of a fully nonlinear 2 × 2 system of conservation laws”, Proceedings of the Edinburgh Mathematical Society, 2012, 1  crossref
    137. P. I. Kogut, R. Manzo, “On Vector-Valued Approximation of State Constrained Optimal Control Problems for Nonlinear Hyperbolic Conservation Laws”, J Dyn Control Syst, 2013  crossref  mathscinet
    138. Ph.G.. LeFloch, Siddhartha Mishra, “Numerical methods with controlled dissipation for small-scale dependent shocks”, Acta Numerica, 23 (2014), 743  crossref  mathscinet  zmath
    139. Alberto Bressan, Wen Shen, “A semigroup approach to an integro-differential equation modeling slow erosion”, Journal of Differential Equations, 2014  crossref  mathscinet
    140. Eric Baer, “Minimizers of Anisotropic Surface Tensions Under Gravity: Higher Dimensions via Symmetrization”, Arch Rational Mech Anal, 2014  crossref  mathscinet
    141. Silvia Jerez, Mario Arciga, “Switch flux limiter method for viscous and nonviscous conservation laws”, Applied Mathematics and Computation, 246 (2014), 292  crossref  mathscinet  zmath
    142. Ting Zhang, Chun Shen, “The shock wave solution to the Riemann problem for the Burgers equation with the linear forcing term”, Applicable Analysis, 2015, 1  crossref  mathscinet
    143. Gaowei CAO, Kai HU, Xiaozhou YANG, “Formula of global smooth solution for non-homogeneous m-d conservation law with unbounded initial value”, Acta Mathematica Scientia, 35:2 (2015), 508  crossref  mathscinet  zmath
    144. Jan Ernest, Ph.G.. LeFloch, Siddhartha Mishra, “Schemes with Well-Controlled Dissipation”, SIAM J. Numer. Anal, 53:1 (2015), 674  crossref  mathscinet  zmath
    145. Francois James, Nicolas Vauchelet, “Numerical Methods for One-Dimensional Aggregation Equations”, SIAM J. Numer. Anal, 53:2 (2015), 895  crossref  mathscinet  zmath
    146. M.R.. Sahoo, “Generalized solution to a system of conservation laws which is not strictly hyperbolic”, Journal of Mathematical Analysis and Applications, 2015  crossref  mathscinet
    147. Yu. G. Rykov, O. B. Feodoritova, “Systems of quasilinear conservation laws and algorithmization of variational principles”, Comput. Math. Math. Phys., 55:9 (2015), 1554–1566  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    148. Yu. G. Rykov, “On the variational approach to systems of quasilinear conservation laws”, Proc. Steklov Inst. Math., 301 (2018), 213–227  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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