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Applicable Analysis
An International Journal
Volume 86, 2007 - Issue 10
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Original Articles

Long-time behavior of solutions of some doubly nonlinear equation

Pages 1265-1281 | Received 09 Mar 2007, Accepted 01 Aug 2007, Published online: 21 Sep 2010

References

  • Alt , HW and Luckhaus , S . 1983 . Quasilinear elliptic–parabolic differential equation . Mathematische Zeitschrift , 183 ( 3 ) : 311 – 341 .
  • Babin , AV and Vishik , MI . 1992 . Attractors of Evolution Equations , Amsterdam : North-Holland .
  • Blanchard , D and Francfort , GA . 1991 . A few results on a class of degenerate parabolic equations . Annali della Scuola Normale Superiore di Pisa, Serie IV , 18 ( 2 ) : 213 – 249 .
  • Carvalho , AN , Cholewa , JW and Dlotko , T . 1999 . Global attractors for problems with monotone operators . Bolletino della Unione Matematica Italiana. Serie VIII. Sezione B. Articoli di Ricerca Matematica , 2 ( 8 ) : 693 – 706 .
  • Carvalho , AN and Gentile , CB . 2003 . Asymptotic behavior of nonlinear parabolic equations with monotone principal part . Journal of Mathematical Analysis and Applications , 280 : 252 – 272 .
  • Dahlberg , BEJ and Kenig , CE . 1993 . Weak solutions of the porous medium equation . Transactions of the American Mathematical Society , 336 ( 2 ) : 711 – 725 .
  • DiBenedetto , E and Vespri , V . 1995 . On the singular equation β(u) t = Δu . Archive for Rational Mechanics and Analysis , 132 ( 3 ) : 247 – 309 .
  • Eden , A and Rakotoson , J-M . 1994 . Exponential attractors for a doubly non-linear equation . Journal of Mathematical Analysis and Applications , 185 : 321 – 339 .
  • Gentile , CB and Primo , M . 2004 . Parameter dependent quasi-linear parabolic equations . Nonlinear Analysis , 59 : 801 – 812 .
  • Gilbarg , D and Trudinger , NS . 1983 . Elliptic Partial Differential Equations of Second Order , Berlin, New York : Springer-Verlag .
  • Goldstein , JA and Zhang , QS . 2001 . On a degenerate heat equation with a singular potential . Journal of Functional Analysis , 186 : 342 – 359 .
  • Igbida , N . 2001 . Large time behavior of solutions to some degenerate parabolic equations. . Communications in Partial Differential Equations , 26 ( 7–8 ) : 1385 – 1408 .
  • Ivanov , AV . 1995 . Existence and uniqueness of a regular solution of the Cauchy-Dirichlet problem for doubly nonlinear parabolic equations . Zeitschrift für Analysis und ihre Anwendungen , 14 ( 4 ) : 751 – 777 .
  • Kacur , J . 1990 . On a solution of degenerate elliptic-parabolic system in Orlicz–Sobolev Spaces I . Mathematische Zeitschrift , 203 ( 1 ) : 153 – 171 . II, Mathematische Zeitschrift, 203(3), 569–579.
  • Khanmamedov , AKh . 2006 . Existence of a global attractor for the parabolic equation with nonlinear Laplacian principal part in an unbounded domain. . Journal of Mathematical Analysis and Applications , 316 ( 2 ) : 601 – 615 .
  • Ladyzhenskaya , OA . 1987 . Finding minimal global attractors for the Navier-Stokes equations and other partial differential equations . Uspekhi Matematicheskikh Nauk , 42 ( 6 ) : 25 – 60 . (Russian).
  • Laptev , GI . 1997 . Weak solutions of second-order quasilinear parabolic equations with double nonlinearity . Sbornik Mathematics , 188 ( 9 ) : 83 – 12 . ; Sbornik Mathematics, 188(9), 1343–1370 (translation).
  • Lions , J-L . 1969 . Quelques Methodes de Resolution des Problemes aux Limites Nonlineaires , Paris : Dunod, Gauthier Villars .
  • Novruzov , EB . 1996 . On smooth solubility of unstable filtration-type equations . Trudy Instituta Matematiki i Mekhaniki , 6 : 179 – 183 . (Russian).
  • Porzio , MM . 1997 . L ∞-regularity for degenerate and singular anisotropic parabolic equations. . Bolletino della Unione Matematica Italiana , 7 ( 11-A ) : 697 – 707 .
  • Sachs , P . 1983 . The initial and boundary value problem for a class of degenerate parabolic equations . Communications in Partial Differential Equations , 8 : 693 – 734 .
  • Soltanov , KN . 2003 . On some modification of the Navier–Stokes equations . Nonlinear Analysis , 52 ( 3 ) : 769 – 793 .
  • Soltanov , KN . 1993 . Existence and nonexistence of global solutions to some nonlinear elliptic-parabolic equations . Differentsial’nye Uravneniya , 29 : 646 – 661 . English transl., Differential Equations, 29, 550–563.
  • Soltanov , KN and Novruzov , EB . 2002 . On a free boundary problem; English transl. . Izvestiya: Mathematics (Izvestiya RAN. , 66 ( 4 ) : 807 – 827 .
  • Soltanov , KN . 2006 . Some nonlinear equations of the nonstable filtration type and embedding theorems . Nonlinear Analysis , 65 ( 11 ) : 2103 – 2134 .
  • Takeuchi , S and Yokota , T . 2003 . Global attractors for a class of degenerate difiusion equations. . Electronic Journal of Differential Equations , 76 : 1 – 13 .
  • Temam , R . 1988 . “ Infinite dimensional dynamical systems in mechanics and physics. ” . In Applied Mathematical Sciences , Vol. 68 , New-York : Springer-Verlag .
  • Yang , M , Sun , Ch and Zhong , Ch . 2007 . Global attractors for p-Laplacian equation. . Journal of Mathematical Analysis and Applications , 327 ( 2 ) : 1130 – 1142 .
  • Yosida , K . 1965 . Functional Analysis , Berlin : Springer-Verlag .

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