A time-fractional space-nonlocal reaction-diffusion equation in a bounded domain is considered. First, the existence of a unique local mild solution is proved. Applying Poincaré inequality it is obtained the existence and boundedness of global classical solution for small initial data. Under some conditions on the initial data, we show that solutions may experience blow-up in a finite time.
Caputo derivative, reaction-diffusion equation, involution, global existence, blow-up
TAPDIGOĞLU, RAMİZ and TOREBEK, BERIKBOL
"Global existence and blow-up of solutions of the time-fractional space-involution reaction-diffusion equation,"
Turkish Journal of Mathematics: Vol. 44:
3, Article 24.
Available at: https://journals.tubitak.gov.tr/math/vol44/iss3/24