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Applicable Analysis
An International Journal
Volume 86, 2007 - Issue 6
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Original Articles

The interface blow-up phenomenon and local estimates for doubly degenerate parabolic equations

Pages 755-782 | Received 04 Apr 2007, Accepted 04 May 2007, Published online: 27 Jun 2007

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A.V. Martynenko. (2016) Fujita-type theorems for doubly degenerate parabolic equations with a time-weighted source. Applicable Analysis 95:5, pages 1050-1058.
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Daniele Andreucci & Anatoli F. Tedeev. (2021) Asymptotic Properties of Solutions to the Cauchy Problem for Degenerate Parabolic Equations with Inhomogeneous Density on Manifolds. Milan Journal of Mathematics 89:2, pages 295-327.
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D. Andreucci & A. F. Tedeev. 2021. Operator Theory and Differential Equations. Operator Theory and Differential Equations 1 6 .
Sujun Weng. (2019) On a weak solution matching up with the double degenerate parabolic equation. Boundary Value Problems 2019:1.
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Roberto Gianni, Anatoli Tedeev & Vincenzo Vespri. (2016) Asymptotic expansion of solutions to the Cauchy problem for doubly degenerate parabolic equations with measurable coefficients. Nonlinear Analysis 138, pages 111-126.
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Sergey Shmarev, Viktor Vdovin & Alexey Vlasov. (2015) Interfaces in diffusion–absorption processes in nonhomogeneous media. Mathematics and Computers in Simulation 118, pages 360-378.
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Emil Novruzov. (2015) Blow-up phenomena for polytropic equation with inhomogeneous density and source. Journal of Mathematical Physics 56:4.
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Razvan Gabriel Iagar & Ariel Sánchez. (2014) Large time behavior for a porous medium equation in a nonhomogeneous medium with critical density. Nonlinear Analysis: Theory, Methods & Applications 102, pages 226-241.
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Pan Zheng & Chunlai Mu. (2013) Global existence, large time behavior, and life span for a degenerate parabolic equation with inhomogeneous density and source. Zeitschrift für angewandte Mathematik und Physik 65:3, pages 471-486.
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PAN ZHENG & CHUNLAI MU. (2014) COMPLETE BLOW-UP AND ESTIMATE ON THE LOCALIZATION FOR A QUASILINEAR PARABOLIC EQUATION WITH NONLINEAR SOURCE. Analysis and Applications 12:02, pages 209-225.
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A. V. Martynenko, A. F. Tedeev & V. N. Shramenko. (2013) On the behavior of solutions of the Cauchy problem for a degenerate parabolic equation with source in the case where the initial function slowly vanishes. Ukrainian Mathematical Journal 64:11, pages 1698-1715.
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Razvan Gabriel Iagar, Guillermo Reyes & Ariel Sánchez. (2012) Radial Equivalence of Nonhomogeneous Nonlinear Diffusion Equations. Acta Applicandae Mathematicae 123:1, pages 53-72.
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Stanislav Antontsev, Michel Chipot & Sergey Shmarev. (2012) Uniqueness and comparison theorems for solutions of doubly nonlinear parabolic equations with nonstandard growth conditions. Communications on Pure and Applied Analysis 12:4, pages 1527-1546.
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Aleksandr V Martynenko, Anatoli F Tedeev & Vladimir N Shramenko. (2012) The Cauchy problem for a degenerate parabolic equation with inhomogeneous density and source in the class of slowly decaying initial data. Izvestiya: Mathematics 76:3, pages 563-580.
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CHUNLAI MU, PAN ZHENG & DENGMING LIU. (2012) LOCALIZATION OF SOLUTIONS TO A DOUBLY DEGENERATE PARABOLIC EQUATION WITH A STRONGLY NONLINEAR SOURCE. Communications in Contemporary Mathematics 14:03, pages 1250018.
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Haifeng Shang & Lihua Deng. (2012) Local and global existence for quasilinear parabolic systems with a strongly nonlinear source. Nonlinear Analysis: Theory, Methods & Applications 75:10, pages 4014-4024.
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Changchun Liu. (2010) Critical exponent for a quasilinear parabolic equation with inhomogeneous density in a cone. Monatshefte für Mathematik 165:2, pages 237-249.
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Александр Валерьевич Мартыненко, Aleksandr Valer'evich Martynenko, Анатолий Федорович Тедеев, Anatoli Fedorovich Tedeev, Владимир Николаевич Шраменко & Vladimir Nikolaevich Shramenko. (2012) Задача Коши для вырождающегося параболического уравнения с неоднородной плотностью и источником в классе медленно стремящихся к нулю начальных функцийThe Cauchy problem for a degenerate parabolic equation with inhomogeneous density and source in the class of slowly decaying initial data. Известия Российской академии наук. Серия математическая Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya 76:3, pages 139-156.
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Honglei Lang, Changchun Liu & Zhenbang Li. (2011) Some properties of solutions for an evolution p(x)-Laplacian equation. Lobachevskii Journal of Mathematics 32:1, pages 48-60.
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P. Cianci, A.V. Martynenko & A.F. Tedeev. (2010) The blow-up phenomenon for degenerate parabolic equations with variable coefficients and nonlinear source. Nonlinear Analysis: Theory, Methods & Applications 73:7, pages 2310-2323.
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