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Nonexistence of Global Solutions of Systems of Time Fractional Differential equations posed on the Heisenberg group
  • Mokhtar Kirane,
  • alrazi abdeljabbar
Mokhtar Kirane
Khalifa University of Science and Technology

Corresponding Author:[email protected]

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alrazi abdeljabbar
Khalifa University of Science and Technology
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Abstract

We first consider the nonlinear time fractional diffusion equation D^{1+α}u+D^β u−∆_{H} u=|u|^p posed on the Heisenberg group H, where 1 < p is a positive real nimber to be specified later; D^δ_{0|t} is the Liouville-Caputo derivative of order δ. For 0 < α < 1,0 < β ≤ 1. This equation interpolates the heat equation and the wave equation with the linear damping D^β_{0|t}u. We present the Fujita exponent for blow-up. Then establish sufficient conditions ensuring non-existence of local solutions. We extend the analysis to the case of the system D^{1+α}u+D^β u−∆_{H} u=|v|^q D^{1+δ}v+D^γ v−∆_{H} v=|u|^p. Our method of proof is based on the nonlinear capacity method.
14 Nov 2021Submitted to Mathematical Methods in the Applied Sciences
15 Nov 2021Submission Checks Completed
15 Nov 2021Assigned to Editor
19 Nov 2021Reviewer(s) Assigned
05 Jan 2022Review(s) Completed, Editorial Evaluation Pending
06 Jan 2022Editorial Decision: Revise Minor
26 Jan 20221st Revision Received
27 Jan 2022Assigned to Editor
27 Jan 2022Submission Checks Completed
28 Jan 2022Reviewer(s) Assigned
30 Jan 2022Review(s) Completed, Editorial Evaluation Pending
03 Feb 2022Editorial Decision: Revise Minor
13 Feb 20222nd Revision Received
16 Feb 2022Submission Checks Completed
16 Feb 2022Assigned to Editor
16 Feb 2022Reviewer(s) Assigned
17 Feb 2022Review(s) Completed, Editorial Evaluation Pending
02 Mar 2022Editorial Decision: Accept
Aug 2022Published in Mathematical Methods in the Applied Sciences volume 45 issue 12 on pages 7336-7345. 10.1002/mma.8243