一类具有梯度项的非线性抛物方程的爆破

The Blowing up of a Class of Nonlinear Parabolic Equations with Gradient Terms

通过引入特征函数和构造适当的爆破因子,讨论了一类具有梯度项的非线性抛物方程的行为,并证明了这类方程初边值问题在有限的时间内爆破.

In the paper, a class of nonlinear parabolic equations with gradient is discussed. By constructing proper blow up factor and introducting the eigenfuction, we prove the solutions of the initial boundary value problems to the equations blow up in finite time.