一类具有正初始能量的双重退化方程解的爆破和爆破时间上界估计

Blow-up and upper bounds of blow-up time fora doubly degenerate equation with positive initial energy

研究了具有齐次Dirichlet边界条件的双重退化抛物方程u t=div(|Δu^(m)|^(p-2)Δu^(m))+f(u),x∈Ω,t≥0解的爆破问题.利用构造凸函数的方法,证明了f在适当的条件下,r>p>2,m≥1,初始能量为正时,解在有限时刻爆破,并给出了爆破时间的上界估计.该结论推广了已有结果.

This paper deals with the blow-up of solutions to the following doubly degenerate parabolic equation u t=div(|Δu^(m)|^(p-2)Δu^(m))+f(u),x∈Ω,t≥0,with homogeneous Dirichlet boundary condition.A blow-up result is established when the initial energy is positive,r>p>2,m≥1,and under suitable conditions on f.Furthermore,a upper bound for blow-up time is also given.This result extends existing results.