Critical exponents of Fujita type for certain time-fractional diffusion equations

  • M. Borikhanov al-Farabi Kazakh National University, Almaty, Kazakhstan
  • B. T. Torebek Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

Abstract

 Solutions of initial value problems for non-linear parabolic partial differential equations may not exist for all time. In other words, these solutions may blow up in some sense or other. Recently in connection with problems for some class of non-linear parabolic equations, Kaplan [1], Ito [2] and Friedman [3] gave certain sufficient conditions under which the solutions blow up in a finite time. Although their results are not identical, we can say according to them that the solutions are apt to blow up when the initial values are sufficiently large. The data at which solutions can blow up is called critical exponents of Fujita. The present paper is devoted to research critical exponents of Fujita type for certain non-linear time-fractional diffusion equations with the nonnegative initial condition. The Riemann-Liouville derivative is used as a fractional derivative. To prove the blow up, we use the known test function method developed in papers by Mitidieri and Pohozhaev [16].

 
 


 
 
 


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Published
Dec 29, 2018
How to Cite
BORIKHANOV, M.; TOREBEK, B. T.. Critical exponents of Fujita type for certain time-fractional diffusion equations. International Journal of Mathematics and Physics, [S.l.], v. 9, n. 2, p. 43-49, dec. 2018. ISSN 2409-5508. Available at: <http://ijmph.kaznu.kz/index.php/kaznu/article/view/262>. Date accessed: 21 mar. 2019.