  The purpose of the article is to study the existence, regularity,
stabilization and blow up results of weak solution to the following parabolic
$(p,q)$-singular equation:
  \begin{equation*}
  (P_t)\; \left\{\begin{array}{rllll}
  u_t-\Delta_{p}u -\Delta_{q}u & = \vth \; u^{-\de}+ f(x,u), \; u>0 \text{ in }
\Om\times (0,T), \\ u&=0 \quad \text{ on } \pa\Om\times (0,T),
  u(x,0)&= u_0(x) \; \text{ in }\Om,
  \end{array}
  \right.
  \end{equation*}
  where $\Om$ is a bounded domain in $\mathbb{R}^N$ with $C^2$ boundary
$\pa\Om$, $1<q<p< \infty$, $0<\de, T>0$, $N\ge 2$ and $\vth>0$ is a parameter.
Moreover, we assume that $f:\Om\times [0,\infty) \to \mb R$ is a bounded below
Carath\'eodory function, locally Lipschitz with respect to the second variable
uniformly in $x\in\Om$ and $u_0\in L^\infty(\Om)\cap W^{1,p}_0(\Om)$. We
distinguish the cases as $q$-subhomogeneous and $q$-superhomogeneous depending
on the growth of $f$ (hereafter we will drop the term $q$). In the
subhomogeneous case, we prove the existence and uniqueness of the weak solution
to problem $(P_t)$ for $\de<2+1/(p-1)$. For this, we first study the stationary
problems corresponding to $(P_t)$ by using the method of sub and super
solutions and subsequently employing implicit Euler method, we obtain the
existence of a solution to $(P_t)$. Furthermore, in this case, we prove the
stabilization result, that is, the solution $u(t)$ of $(P_t)$ converges to
$u_\infty$, the unique solution to the stationary problem, in $L^\infty(\Om)$
as $t\ra\infty$. For the superhomogeneous case, we prove the local existence
theorem by taking help of nonlinear semigroup theory. Subsequently, we prove
finite time blow up of solution to problem $(P_t)$ for small parameter
$\vartheta>0$ in the case $\de\leq 1$ and for all $\vth>0$ in the case $\de>1$.
