In this paper, we investigate the blow-up phenomena for the following reaction-diffusion model with nonlocal and gradient terms: {u(t) = Delta u + au(p) (integral(Omega) u(alpha) dx)(m) - vertical bar del u vertical bar(q) in Omega x (0, t*) partial derivative u/partial derivative v = h(u) on partial derivative Omega x (0, t*) u(x, 0) = u(0) (x) >= 0 in (Omega) over bar. Here Omega subset of R-N (N >= 3) is a bounded and convex domain with smooth boundary, and constants m, p, q, alpha are supposed to be positive. Utilizing the Sobolev inequality and the differential inequality technique, lower bound for blow-up time is derived when blow-up occurs. In addition, we give an example as application to illustrate the abstract results obtained in this paper.
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