Existence and nonexistence of solutions for \(u_ t=\text{div}(|\nabla u|^{p-2}\nabla u)+f(\nabla u,u,x,t)\) (Q2367730)

We investigate the existence and nonexistence of global solutions for the initial and boundary value problem \[ u_ t= \text{div} (|\nabla u|^{p-2} \nabla u)+ f(\nabla u,u,x,t), \qquad (x,t)\in Q_ T, \] \[ u(x,0)= u_ 0(x), \quad x\in\Omega, \qquad u(x,t)=0, \quad x\in \partial\Omega, \] where \(p>2\), \(Q_ T= \Omega\times (0,T)\), and \(\Omega\in \mathbb{R}^ N\) is a bounded domain with smooth boundary \(\partial\Omega\).