TY - ELEC
AU - Showalter, Ralph E.
PY - 2018
TI - A Pseudo-Parabolic PDE for Compaction of a Sedimentary Basin
LA - eng
M3 - Moving Image
AB - The porosity of a compacting sedimentary basin satisfies a nonlinear
pseudo-parabolic partial differential equation. This equation is
distinguished from the classical porous medium equation by a third
order term, a degenerate elliptic operator in spatial variables acting
on the time derivative of the solution. We describe the derivation of
the model equation, review classical results for pseudo-parabolic
equations and their relation to parabolic equations, present new
existence and regularity results for this nonlinear PDE, and show they
are consistent with expected behavior of solutions in this context.
N2 - The porosity of a compacting sedimentary basin satisfies a nonlinear
pseudo-parabolic partial differential equation. This equation is
distinguished from the classical porous medium equation by a third
order term, a degenerate elliptic operator in spatial variables acting
on the time derivative of the solution. We describe the derivation of
the model equation, review classical results for pseudo-parabolic
equations and their relation to parabolic equations, present new
existence and regularity results for this nonlinear PDE, and show they
are consistent with expected behavior of solutions in this context.
UR - https://open.library.ubc.ca/collections/48630/items/1.0377033
ER - End of Reference