Existence and blow-up of solutions in Hénon-type heat equation with exponential nonlinearity

In the present article, we are concerned with the following problem: vt=Δv+∣x∣βev,x∈RN,t>0,v(x,0)=v0(x),x∈RN,\left\{\phantom{\rule[-1.25em]{}{0ex}}\begin{array}{ll}{v}_{t}=\Delta v+| x{| }^{\beta }{e}^{v},\hspace{1.0em}& x\in {{\mathbb{R}}}^{N},\hspace{0.33em}t\gt 0,\\ v\left(x,0)={v}_{0}\left(x),\hspace{1.0em}& x\in {{\mathbb{R}}}^{N},\end{array}\right. where N≥3N\ge 3, 0