Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Physical Sciences and Mathematics
Quenching Estimates For A Non-Newtonian Filtration Equation With Singular Boundary Conditions, Matthew Beauregard, Burhan Selcuk
Quenching Estimates For A Non-Newtonian Filtration Equation With Singular Boundary Conditions, Matthew Beauregard, Burhan Selcuk
Faculty Publications
In this paper, the quenching behavior of the non-Newtonian filtration equation (φ(u))t = (|ux| r−2 ux)x with singular boundary conditions, ux (0, t) = u −p (0, t), ux (a, t) = (1 − u(a, t))−q is investigated. Various conditions on the initial condition are shown to guarantee quenching at either the left or right boundary. Theoretical quenching rates and lower bounds to the quenching time are determined when φ(u) = u and r = 2. Numerical experiments are provided to illustrate and provide additional validation of the theoretical estimates to the quenching rates and times.