Blow-up phenomena in a class of coupled reaction-diffusion system with nonlocal boundary conditions

The paper deals with blow-up phenomena for the following coupled reaction-diffusion system with nonlocal boundary conditions: {ut = del . (rho(1)(u)del u) + a(1)(x)F-1(v) (x,t) is an element of D x (0, T), v(t) = del . (rho(2)(u)del v) + a(2)(x)F-2(u) (x,t) is an element of D x (0, T), partial derivative u/partial derivative v = k(1)(t) integral(D)g(1)(u)dx, partial derivative v/partial derivative v = k(2)(t)integral(D)g(2)(v)dx, (x,t) is an element of partial derivative D x (0, T), u(x,0) = u(0)(x), v(x, 0) = v(0)(x), x is an element of (D) over bar Based on some differential inequalities and Sobolev inequality, we establish conditions on the data to guarantee the occurrence of the blow-up. Moreover, when the blow-up occurs, explicit lower and upper bounds on blow-up time are obtained. At last, an example is presented to illustrate our main results. 2021 Published by Elsevier Inc.