论文标题
半线性热方程式的关键富士气指数具有退化系数
Critical Fujita exponent for a semilinear heat equation with degenerate coefficients
论文作者
论文摘要
我们证明存在涉及退化系数的非均匀半线性热方程的关键富士塔指数。更准确地说，为了提供一个相当完整的理论，我们专注于两种类型的权重$ W（x）= | x_1 |^a $或$ w（x）= | x |^b $其中$ a，$ a，b> 0 $在合适的范围内。所考虑的系数承认起源或奇异性线的奇异性。在后一种情况下，问题与分数laplacian有关。
We prove the existence of a critical Fujita exponent for a non-homogeneous semilinear heat equation which involves degenerate coefficients. More precisely, in order to give a rather complete theory, we focus on two types of weights $w(x)=|x_1|^a$ or $w(x)=|x|^b$ where $a, b>0$ in a suitable range. The coefficients under consideration admit either a singularity at the origin or a line of singularities. In the latter case, the problem is related to the fractional Laplacian.
