On a general degenerate/singular parabolic equation with a nonlocal space term

Autor: Brahim Allal, Genni Fragnelli, Jawad Salhi
Rok vydání: 2023
Předmět:
Zdroj: Mathematical Methods in the Applied Sciences.
ISSN: 1099-1476
0170-4214
DOI: 10.1002/mma.9190
Popis: 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.
Databáze: OpenAIRE
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