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Zapiski Nauchnykh Seminarov POMI, 1999, Volume 259, Pages 67–88 (Mi znsl1051)  

This article is cited in 7 scientific papers (total in 7 papers)

Existence and uniqueness of a weak solution to the initial mixt boundary value problem for quasilinear elliptic-parabolic equations

A. V. Ivanova, J.-F. Rodriguesb

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
b Universidade de Lisboa
Full-text PDF (234 kB) Citations (7)
Abstract: We prove the existence and the uniqueness of a weak solution to the mixed boundary problem for the elliptic-parabolic equation
tb(u)div{|σ(u)|m2σ(u)}=f(x,t),δ(u):=u+k(b(u))e,|e|=1,\enskipm>1,
with a monotone nondecreasing continuous function b. Such equations arise in the theory of non-Newtonian filtration as well as in the mathematical glaciology.
Received: 08.04.1999
English version:
Journal of Mathematical Sciences (New York), 2002, Volume 109, Issue 5, Pages 1851–1866
DOI: https://doi.org/10.1023/A:1014488123746
Bibliographic databases:
UDC: 517.9
Language: English
Citation: A. V. Ivanov, J.-F. Rodrigues, “Existence and uniqueness of a weak solution to the initial mixt boundary value problem for quasilinear elliptic-parabolic equations”, Boundary-value problems of mathematical physics and related problems of function theory. Part 30, Zap. Nauchn. Sem. POMI, 259, POMI, St. Petersburg, 1999, 67–88; J. Math. Sci. (New York), 109:5 (2002), 1851–1866
Citation in format AMSBIB
\Bibitem{IvaRod99}
\by A.~V.~Ivanov, J.-F.~Rodrigues
\paper Existence and uniqueness of a weak solution to the initial mixt boundary value problem for quasilinear
elliptic-parabolic equations
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~30
\serial Zap. Nauchn. Sem. POMI
\yr 1999
\vol 259
\pages 67--88
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1051}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1754358}
\zmath{https://zbmath.org/?q=an:0983.35094}
\transl
\jour J. Math. Sci. (New York)
\yr 2002
\vol 109
\issue 5
\pages 1851--1866
\crossref{https://doi.org/10.1023/A:1014488123746}
Linking options:
  • https://www.mathnet.ru/eng/znsl1051
  • https://www.mathnet.ru/eng/znsl/v259/p67
  • This publication is cited in the following 7 articles:
    1. Antontsev S., Chipot M., Shmarev S., “Uniqueness and Comparison Theorems for Solutions of Doubly Nonlinear Parabolic Equations with Nonstandard Growth Conditions”, Commun. Pure Appl. Anal, 12:4 (2013), 1527–1546  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    2. Kiyeon Shin, Sujin Kang, “DOUBLY NONLINEAR VOLTERRA EQUATIONS INVOLVING THE LERAY-LIONS OPERATORS”, East Asian mathematical journal, 29:1 (2013), 69  crossref
    3. Michal Beneš, “A Note on Doubly Nonlinear Parabolic Systems with Unilateral Constraint”, Results. Math., 63:1-2 (2013), 47  crossref
    4. Antontsev S., Shmarev S., “Elliptic equations with triple variable nonlinearity”, Complex Variables and Elliptic Equations, 56:7–9 (2011), 573–597  crossref  mathscinet  zmath  isi  scopus  scopus
    5. Antontsev S., Shmarev S., “Parabolic equations with double variable nonlinearities”, Math Comput Simulation, 81:10 (2011), 2018–2032  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    6. Kang S., “Doubly nonlinear Volterra equations related to the p-Laplacian operator”, Math Methods Appl Sci, 34:9 (2011), 1065–1074  crossref  mathscinet  zmath  isi  scopus  scopus
    7. Antontsev S.N., De Oliveira H.B., “On a mathematical model in ice sheet dynamics”, Proceedings of the 5th Iasme/Wseas International Conference on Fluid Mechanics and Aerodynamics (Fma '07), Mathematics and Computers in Science and Engineering, 2007, 1–8  isi
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