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

摘要

The paper deals with blow-up phenomena for the following coupled reaction-diffusion system with nonlocal boundary conditions:{ut=∇·(ρ1(u)∇u)+a1(x)f1(v),(x,t)∈D×(0,T),vt=∇·(ρ2(v)∇v)+a2(x)f2(u),(x,t)∈D×(0,T),∂u∂ν=k1(t)∫Dg1(u)dx,∂v∂ν=k2(t)∫Dg2(v)dx,(x,t)∈∂D×(0,T),u(x,0)=u0(x),v(x,0)=v0(x),x∈D¯.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.