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The Fujita and Secondary Type Critical Exponents in Nonlinear Parabolic Equations and Systems

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Differential Equations and Dynamical Systems (USUZCAMP 2017)

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Abstract

In this work, demonstrated the possibilities of the self-similar approach to the studying of qualitative properties of nonlinear reaction diffusion equation and system such as finite speed of a perturbation, Fujita and secondary type critical exponents of a global solvability. Asymptotic of the self-similar solutions in a secondary critical case is established. Based on the computer modeling of nonlinear processes described by nonlinear degenerate parabolic equation and cross system discussed. The problem choosing an initial approximation for numerical solution depending on a value of numerical parameters is solved.

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Authors and Affiliations

  1. National university of Uzbekistan, Tashkent, Uzbekistan

    Aripov Mersaid

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  1. Aripov Mersaid
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Correspondence to Aripov Mersaid .

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Editors and Affiliations

  1. Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan

    Abdulla Azamov

  2. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, USA

    Leonid Bunimovich

  3. Turin Polytechnic University, Tashkent, Uzbekistan

    Akhtam Dzhalilov

  4. Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA, USA

    Hong-Kun Zhang

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Mersaid, A. (2018). The Fujita and Secondary Type Critical Exponents in Nonlinear Parabolic Equations and Systems. In: Azamov, A., Bunimovich, L., Dzhalilov, A., Zhang, HK. (eds) Differential Equations and Dynamical Systems. USUZCAMP 2017. Springer Proceedings in Mathematics & Statistics, vol 268. Springer, Cham. https://doi.org/10.1007/978-3-030-01476-6_2

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