How can I show that \int_{0}^{t}\int_{M}|\nabla u^{q}|^{p}\leq t \int_{M}|\nabla u^{q}|^{p}(0) for weak solutions of \partial_{t}u=\Delta_{p}u^{q} on a Riemannian manifold without using the monotonicty of the function \int_{M}|\nabla u^{q}|^{p}(t)?
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