Existence and Nonexistence of the Solutions to the Cauchy Problem of Quasilinear Parabolic Equation with a Gradient Term
Existence and Nonexistence of the Solutions to the Cauchy Problem of Quasilinear Parabolic Equation with a Gradient Term
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DOI：
10.1007/s10986-021-09511-2
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发表时间：
2021-01
影响因子：
0.4
通讯作者：
Mingjun Zhou;Yang Leng
中科院分区：
文献类型：
--
作者：
Mingjun Zhou;Yang Leng
本文讨论了一类带梯度项的拟线性抛物型方程Cauchy问题解的存在性和不存在性。我们建立了Fujita型爆破定理，并确定了临界Fujita指数的空间维度，在无穷远的梯度项的系数的渐近行为，在时间导数项的系数的空间位置的指数，和源项。特别地，我们将临界情况归类为爆发情况。
This paper deals with the existence and non-xistence of the solutions to the Cauchy problem of a class of quasilinear parabolic equations with a gradient term. We establish Fujita-type blowup theorems and determine the critical Fujita exponent in terms of spatial dimension, the asymptotic behavior of the coefficients of the gradient term at infinity, the exponents of spatial positions in the coefficients of the time-derivative term, and the source term. In particular, we classify the critical case as the blowup case.