On nonlinear nonlocal systems of reaction diffusion equations. (English) Zbl 1474.35627

Ahmad, B.; Alhothuali, M. S.; Alsulami, H. H.; Kirane, M.; Timoshin, S.

Abstr. Appl. Anal. 2014, Article ID 804784, 6 p. (2014).

Summary: The reaction diffusion system with anomalous diffusion and a balance law \(u_t + \left(- \Delta\right)^{\alpha / 2} u = - f \left(u, v\right)\), \(v_t + \left(- \Delta\right)^{\beta / 2} v = f \left(u, v\right)\), \(0 < \alpha\), \(\beta < 2\), is con sidered. The existence of global solutions is proved in two situations: (i) a polynomial growth condition is imposed on the reaction term \(f\) when \(0 < \alpha \leq \beta \leq 2\); (ii) no growth condition is imposed on the reaction term \(f\) when \(0 < \beta \leq \alpha \leq 2\).

MSC:

35R11	Fractional partial differential equations
35A01	Existence problems for PDEs: global existence, local existence, non-existence

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