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Mat. Sb., 2000, Volume 191, Number 9, Pages 43–64 (Mi msb506)  

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

Evolution equations with monotone operator and functional non-linearity at the time derivative

G. I. Laptev

Tula State University

Abstract: Conditions for the solubility of the so-called doubly non-linear equations
$$ Au+\frac\partial{\partial t}Bu=f, \qquad u(0)=u_0, $$
are investigated. Here $A$ is a monotone operator induced by a differential expression containing higher-order partial derivatives and $B$ is an operator induced by a monotone function. A theorem on the existence of a solution is proved. The method of monotone operators is used in combination with the method of compact operators. Examples of applications to parabolic differential equations are presented.

DOI: https://doi.org/10.4213/sm506

Full text: PDF file (323 kB)
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English version:
Sbornik: Mathematics, 2000, 191:9, 1301–1322

Bibliographic databases:

UDC: 517.9
MSC: 35K90, 35K65
Received: 13.03.1999

Citation: G. I. Laptev, “Evolution equations with monotone operator and functional non-linearity at the time derivative”, Mat. Sb., 191:9 (2000), 43–64; Sb. Math., 191:9 (2000), 1301–1322

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. Kuznetsov A.V., “Solvability of doubly nonlinear evolution equations with monotone operators”, Differ. Equ., 39:9 (2003), 1237–1248  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    2. Laptev G.I., Lapteva N.A., “Usloviya monotonnosti operatorov Nemytskogo so stepennymi nelineinostyami”, Uchenye zapiski Rossiiskogo gos. sotsialnogo un-ta, 2009, no. 7-1, 223–228  elib
    3. Laptev G.I., Lapteva N.A., “Pochti ravnomerno monotonnye operatory banakhovom prostranstve”, Uchenye zapiski Rossiiskogo gos. sotsialnogo un-ta, 2:7 (2009), 214–219  elib
    4. M. O. Korpusov, “Solution blowup for the heat equation with double nonlinearity”, Theoret. and Math. Phys., 172:3 (2012), 1173–1176  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    5. M. O. Korpusov, “Solution blow-up for a class of parabolic equations with double nonlinearity”, Sb. Math., 204:3 (2013), 323–346  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. Korpusov M.O., “Blow-Up of Solutions of a System of Equations with Double Nonlinearities and Nonlocal Sources”, Differ. Equ., 49:12 (2013), 1511–1517  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    7. L. M. Kozhevnikova, A. A. Leont'ev, “Solutions to higher-order anisotropic parabolic equations in unbounded domains”, Sb. Math., 205:1 (2014), 7–44  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. 璟 苏, “Blowup of Solutions for a Class of Doubly Nonlinear Parabolic Equations”, PM, 05:02 (2015), 59  crossref
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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