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On a general degenerate/singular parabolic equation with a nonlocal space term
  • Brahim Allal,
  • Genni Fragnelli,
  • Jawad Salhi
Brahim Allal
Universite Hassan 1er de Settat

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Genni Fragnelli
Università degli Studi di Bari
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Jawad Salhi
Moulay Ismail University of Meknes
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In this paper we study the null controllability for the problems associated to the operators y_t-Ay - \lambda/b(x) y+\int_0^1 K(t,x,\tau)y(t, \tau) d\tau, (t,x) \in (0,T)\times (0,1) where Ay := ay_{xx} or Ay := (ay_x)_x and the functions a and b degenerate at an interior point x0 Ë .0; 1/. To this aim, as a first step we study the well posedness, the Carleman estimates and the null controllability for the associated nonhomogeneous degenerate and singular heat equations. Then,using the Kakutani’s fixed point Theorem, we deduce the null controllability property for the initial nonlocal problems.
05 Dec 2021Submitted to Mathematical Methods in the Applied Sciences
06 Dec 2021Submission Checks Completed
06 Dec 2021Assigned to Editor
11 Dec 2021Reviewer(s) Assigned
05 Jan 2023Review(s) Completed, Editorial Evaluation Pending
05 Jan 2023Editorial Decision: Revise Minor
11 Jan 20231st Revision Received
12 Jan 2023Submission Checks Completed
12 Jan 2023Assigned to Editor
12 Jan 2023Review(s) Completed, Editorial Evaluation Pending
12 Jan 2023Reviewer(s) Assigned
13 Feb 2023Editorial Decision: Accept