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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Volume 261, Pages 16–25 (Mi tm736)  
This article is cited in 35 scientific papers (total in 35 papers)

Extinction of Solutions of Parabolic Equations with Variable Anisotropic Nonlinearities

S. N. Antontsevab, S. I. Shmarevc

a Departamento de Matemática, Universidade da Beira Interior
b Departamento de Matemática Aplicada, Universidad Complutence
c Departaménto de Matemáticas, Universidad de Oviedo
Full-text PDF (202 kB) Citations (35)
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Abstract: We study the Dirichlet problem for a class of nonlinear parabolic equations with nonstandard anisotropic growth conditions that generalize the evolutional $p(x,t)$-Laplacian. We study the property of extinction of solutions in finite time. In particular, we show that the extinction may take place even in the borderline case when the equation becomes linear as $t\to\infty$.
Received in March 2007
English version:
Proceedings of the Steklov Institute of Mathematics, 2008, Volume 261, Pages 11–21
DOI: https://doi.org/10.1134/S0081543808020028
Bibliographic databases:
UDC: 517.956.4
Language: English
Citation: S. N. Antontsev, S. I. Shmarev, “Extinction of Solutions of Parabolic Equations with Variable Anisotropic Nonlinearities”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 261, MAIK Nauka/Interperiodica, Moscow, 2008, 16–25; Proc. Steklov Inst. Math., 261 (2008), 11–21
Citation in format AMSBIB
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    • This publication is cited in the following 35 articles:
    1. Huashui Zhan, “On Multiple Degenerate Parabolic Equation with Variable Exponent”, Acta Appl Math, 196:1 (2025)  crossref
    2. Jingjing Zhang, Xiaolei Li, “Blow-Up and Global Existence of Solutions to Degenerate Kirchhoff Equation with Variable Source”, Mediterr. J. Math., 21:4 (2024)  crossref
    3. Fengjie Li, Anqi Sun, “Singular Solutions in a p(x)-Laplace Equation with Multi-sources”, J Dyn Control Syst, 29:3 (2023), 625  crossref
    4. Benkouider Soufiane, Rahmoune Abita, “Blow-up time analysis of parabolic equations with variable nonlinearities”, Applicable Analysis, 102:18 (2023), 5082  crossref
    5. Liu B., Zhang M., Li F., “Singular Properties of Solutions For a Parabolic Equation With Variable Exponents and Logarithmic Source”, Nonlinear Anal.-Real World Appl., 64 (2022), 103449  crossref  mathscinet  isi
    6. Li F., Sun X., Zhang J., “Qualitative Study in a Parabolic Equation With Nonstandard Growth Conditions and Singular Medium Void”, Bull. Iran Math. Soc., 48:2 (2022), 479–506  crossref  mathscinet  isi
    7. Wang Yu., Liu B., Sun Yu., “Asymptotic Property of Singular Solutions in Some Nonstandard Parabolic Equation”, Nonlinear Anal.-Real World Appl., 60 (2021), 103301  crossref  mathscinet  isi  scopus
    8. Zakaria A., “Stochastic System For Generalized Polytropic Filtration”, Math. Meth. Appl. Sci., 43:1 (2020), 134–173  crossref  mathscinet  isi  scopus
    9. Zhan H., “The Nonnegative Weak Solution of a Degenerate Parabolic Equation With Variable Exponent Growth Order”, Bound. Value Probl., 2020:1 (2020), 69  crossref  mathscinet  isi  scopus
    10. Le Cong Nhan, Quach Van Chuong, Le Xuan Truong, “Potential Well Method For P(X)-Laplacian Equations With Variable Exponent Sources”, Nonlinear Anal.-Real World Appl., 56 (2020), 103155  crossref  mathscinet  isi
    11. Liu B., Dong M., “A Nonlinear Diffusion Problem With Convection and Anisotropic Nonstandard Growth Conditions”, Nonlinear Anal.-Real World Appl., 48 (2019), 383–409  crossref  mathscinet  isi  scopus
    12. Crispo F. Maremonti P. Ruzicka M., “Global l-R-Estimates and Regularizing Effect For Solutions to the P(T, X)-Laplacian Systems”, Adv. Differ. Equat., 24:7-8 (2019), 407–434  mathscinet  isi
    13. Liu B., Xin Q., Dong M., “Blow-Up Analyses in Parabolic Equations With Anisotropic Nonstandard Damping Source”, J. Math. Anal. Appl., 458:1 (2018), 242–264  crossref  mathscinet  zmath  isi  scopus
    14. Giacomoni J., “Quasilinear Parabolic Problem With Variable Exponent: Qualitative Analysis and Stabilization”, Commun. Contemp. Math., 20:8 (2018), 1750065  crossref  mathscinet  zmath  isi  scopus
    15. Liu B., Dong M., Li F., “Singular Solutions in Nonlinear Parabolic Equations With Anisotropic Nonstandard Growth Conditions”, J. Math. Phys., 59:12 (2018), 121504  crossref  mathscinet  zmath  isi  scopus
    16. Bokalo M.M., Ilnytska O.V., “Problems For Parabolic Equations With Variable Exponents of Nonlinearity and Time Delay”, Appl. Anal., 96:7 (2017), 1240–1254  crossref  mathscinet  zmath  isi  scopus
    17. È. R. Andriyanova, F. Kh. Mukminov, “Existence and qualitative properties of a solution of the first mixed problem for a parabolic equation with non-power-law double nonlinearity”, Sb. Math., 207:1 (2016), 1–40  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    18. Liu B., Yang J., “Blow-up properties in the parabolic problems with anisotropic nonstandard growth conditions”, Z. Angew. Math. Phys., 67:1 (2016), UNSP 13  crossref  mathscinet  isi  elib  scopus
    19. Antontsev S., Shmarev S., Simsen J., Simsen M.S., Nonlinear Anal.-Theory Methods Appl., 134 (2016), 31–54  crossref  mathscinet  zmath  isi  scopus
    20. Chai X. Li H. Niu W., “Large Time Behavior For P(X)-Laplacian Equations With Irregular Data”, Electron. J. Differ. Equ., 2015, 61  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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