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Mat. Sb., 1989, Volume 180, Number 9, Pages 1183–1210 (Mi msb1656)  

This article is cited in 10 scientific papers (total in 10 papers)

The Cauchy problem for odd-order quasilinear equations

A. V. Faminskii


Abstract: A nonlocal Cauchy problem for multidimensional quasilinear evolution equations containing a linear differential operator $L(t,x,D_x)$ with leading derivatives of odd order is considered. The conditions on the nonlinear terms are chosen so that they are subordinate to the operator $L$. The Korteweg–de Vries equation is a special case of such equations. No smoothness conditions are imposed on the initial function $u_0(x)$ $(u_0(x)\in L_2(\mathbf R^n))$. Theorems on the existence, uniqueness, and continuous dependence on the initial data of generalized solutions are established.
Bibliography: 20 titles.

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English version:
Mathematics of the USSR-Sbornik, 1991, 68:1, 31–59

Bibliographic databases:

UDC: 517.9
MSC: Primary 35K22; Secondary 35Q20, 35D05
Received: 18.08.1987

Citation: A. V. Faminskii, “The Cauchy problem for odd-order quasilinear equations”, Mat. Sb., 180:9 (1989), 1183–1210; Math. USSR-Sb., 68:1 (1991), 31–59

Citation in format AMSBIB
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\by A.~V.~Faminskii
\paper The Cauchy problem for odd-order quasilinear equations
\jour Mat. Sb.
\yr 1989
\vol 180
\issue 9
\pages 1183--1210
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1017821}
\zmath{https://zbmath.org/?q=an:0701.35046|0712.35085}
\transl
\jour Math. USSR-Sb.
\yr 1991
\vol 68
\issue 1
\pages 31--59
\crossref{https://doi.org/10.1070/SM1991v068n01ABEH001932}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1991EX22700003}


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  • http://mi.mathnet.ru/eng/msb/v180/i9/p1183

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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. K. Sangare, A. V. Faminskii, “Weak Solutions of a Mixed Problem in a Half-Strip for a Generalized Kawahara Equation”, Math. Notes, 85:1 (2009), 90–100  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Kuvshinov R.V., Faminskii A.V., “Mixed problem for the Kawahara equation in a half-strip”, Differ. Equ., 45:3 (2009), 404–415  crossref  mathscinet  zmath  isi  elib  elib
    3. Larkin N.A., Luchesi J., “General Mixed Problems for the KdV Equations on Bounded Intervals”, Electron. J. Differ. Equ., 2010, 168  mathscinet  zmath  adsnasa  isi
    4. Faminskii A.V., Larkin N.A., “Initial-Boundary Value Problems for Quasilinear Dispersive Equations Posed on a Bounded Interval”, Electron. J. Differ. Equ., 2010, 01  mathscinet  zmath  isi  elib
    5. Faminskii A.V., “Weak Solutions to Initial-Boundary-Value Problems for Quasilinear Evolution Equations of an Odd Order”, Adv. Differ. Equat., 17:5-6 (2012), 421–470  mathscinet  zmath  isi
    6. A. V. Faminskii, M. A. Opritova, “On the initial-value problem for the Kawahara equation”, Journal of Mathematical Sciences, 201:5 (2014), 614–633  mathnet  crossref  mathscinet
    7. Larkin N.A., Simoes M.H., “General Boundary Conditions for the Kawahara Equation on Bounded Intervals”, Electron. J. Differ. Equ., 2013, 159  isi
    8. Baykova E.S., Faminskii A.V., “On Initial-Boundary-Value Problems in a Strip for the Generalized Two-Dimensional Zakharov-Kuznetsov Equation”, Adv. Differ. Equat., 18:7-8 (2013), 663–686  isi
    9. A. P. Antonova, A. V. Faminskii, “On the Regularity of Solutions of the Cauchy Problem for the Zakharov–Kuznetsov Equation in Hölder Norms”, Math. Notes, 97:1 (2015), 12–20  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. Faminskii A.V., “Initial-Boundary Value Problems in a Rectangle For Two-Dimensional Zakharov-Kuznetsov Equation”, J. Math. Anal. Appl., 463:2 (2018), 760–793  crossref  isi
  • Математический сборник - 1989–1990 Sbornik: Mathematics (from 1967)
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