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Mat. Sb., 2003, Volume 194, Number 1, Pages 147–160 (Mi msb710)  

This article is cited in 8 scientific papers (total in 9 papers)

Multidimensional scalar conservation laws

S. I. Pokhozhaev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: A new approach, based on a priori estimates, to the demonstration of the occurrence of a gradient catastrophe of solutions of multidimensional scalar conservation laws is considered.
Upper estimates for the time of the gradient catastrophe are derived. A counterexample is presented showing that the estimate so obtained is asymptotically best possible in the general class of problems under consideration.

DOI: https://doi.org/10.4213/sm710

Full text: PDF file (243 kB)
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English version:
Sbornik: Mathematics, 2003, 194:1, 151–164

Bibliographic databases:

UDC: 517.9
MSC: 35L65, 35B05
Received: 07.06.2002

Citation: S. I. Pokhozhaev, “Multidimensional scalar conservation laws”, Mat. Sb., 194:1 (2003), 147–160; Sb. Math., 194:1 (2003), 151–164

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. I. Pokhozhaev, “On a priori Estimates and Gradient Catastrophes of Smooth Solutions to Hyperbolic Systems of Conservation Laws”, Proc. Steklov Inst. Math., 243 (2003), 247–277  mathnet  mathscinet  zmath
    2. Pokhozhaev S.I., “On hyperbolic systems of conservation laws”, Differ. Equ., 39:5 (2003), 701–711  mathnet  crossref  mathscinet  zmath  isi  elib
    3. O. V. Besov, A. M. Il'in, V. A. Il'in, L. D. Kudryavtsev, S. M. Nikol'skii, L. V. Ovsyannikov, E. Mitidieri, A. Tesei, L. Véron, “Stanislav Ivanovich Pokhozhaev (on his 70th birthday)”, Russian Math. Surveys, 61:2 (2006), 373–378  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Pohozaev S.I, “On the nonexistence of global solutions of the Hamilton–Jacobi equation”, Differ. Equ., 44:10 (2008), 1467–1477  crossref  mathscinet  zmath  isi  elib
    5. Pohozaev S.I., “Critical nonlinearities in partial differential equations”, Milan J. Math., 77:1 (2009), 127–150  crossref  mathscinet  zmath  isi  elib
    6. S. I. Pokhozhaev, “Weighted Identities for the Solutions of Generalized Korteweg–de Vries Equations”, Math. Notes, 89:3 (2011), 382–396  mathnet  crossref  crossref  mathscinet  isi
    7. Matus P.P., “On the Role of Conservation Laws in the Problem on the Occurrence of Unstable Solutions for Quasilinear Parabolic Equations and their Approximations”, Differ. Equ., 49:7 (2013), 883–894  crossref  mathscinet  zmath  isi
    8. Pokhozhaev S.I., “Critical Nonlinearities in Partial Differential Equations”, Russ. J. Math. Phys., 20:4 (2013), 476–491  crossref  mathscinet  zmath  isi
    9. Kozera R., Paradzinska A., Schadinskii D., “Numerical Blow-Up Time”, Exact Finite-Difference Schemes, eds. Lemeshevsky S., Matus P., Poliakov D., Walter de Gruyter Gmbh, 2016, 220–232  mathscinet  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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