This paper deals with a nonlinear parabolic equation with a complicated source term, which is a product of localized source $e^{q u(0,t)}$, local source $e^{pu(x, t)}$, and weight function $a(x)$. We investigate how the three factors influence the asymptotic behavior of solutions. We show that the blow-up set consists of single point ${x=0}$ if $p>0$; when $ple 0$ with $p+q>0$, the blow-up takes place everywhere in $B$. Moreover, the blow-up rate estimation is established with precise coefficients determined.
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机译：本文处理具有复杂源项的非线性抛物方程，它是局部源$ e ^ {qu（0，t）} $，局部源$ e ^ {pu（x，t）} $和权重函数$ a（x）$。我们调查这三个因素如何影响解的渐近行为。我们证明，如果$ p> 0 $，则爆炸集合由单点$ {x = 0} $组成；当$ ple 0 $与$ p + q> 0 $时，爆炸在$ B $的任何地方发生。此外，利用确定的精确系数来建立爆破速率估计。
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