Blow-up analysis for a system of heat equations with nonlinear flux which obey different laws Original Research Article

We consider a system of heat equations ut=Δuut=Δu and vt=Δvvt=Δv in Ω×(0,T)Ω×(0,T) completely coupled by nonlinear boundary conditions View the MathML source∂u∂η=epvuα,∂v∂η=uqeβvon ∂Ω×(0,T). Turn MathJax on We prove that the solutions always blow up in finite time for non-zero and non-negative initial values. Also, the blow-up only occurs on ∂Ω∂Ω with View the MathML sourceC1(T−t)−p−β2(pq+β−αβ)≤maxΩ¯u(x,t)≤C2(T−t)−p−β2(pq+β−αβ), Turn MathJax on View the MathML sourcelog(C3(T−t)−q+1−α2(pq+β−αβ))≤maxΩ¯v(x,t)≤log(C4(T−t)−q+1−α2(pq+β−αβ)) Turn MathJax on for p,q>0p,q>0, 0≤α<10≤α<1 and 0≤β