Demand has increased for analytical solutions to determine the velocities and dispersion coefficients that describe solute transport with spatial, temporal, or spatiotemporal variations encountered in field. However, few have considered spatially, temporally, spatiotemporally dependent velocities. The proposed consider eight cases of velocities: both spatially dependent, temporally coefficient ...

In this work, we deal with the m- Laplacian equation time dependent variable coefficients. Under suitable conditions on coefficients, prove blow up of solutions for finite negative initial energy. These results partially generalize and extend some recent ones in previous literature.

<p style='text-indent:20px;'>We consider the initial-value problem for one-dimensional, time-dependent wave equation with positive, Lipschitz continuous coefficients, which are constant outside a bounded region. Under assumption of compact support initial data, we prove that local energy decays exponentially fast in time, and provide explicit to solution converges large times. We give est...