Selcuk, Burhan2024-09-292024-09-2920220049-29302073-9826https://doi.org/10.5556/j.tkjm.53.2022.3853https://hdl.handle.net/20.500.14619/7834This paper studies the following two porous medium equations with singular boundary conditions. First, we obtain that finite time quenching on the boundary, as well as k(t) blows up at the same finite time and lower bound estimates of the quenching time of the equation k(t) = (k(n))(xx) + (1 - k)(-alpha), (x, t) is an element of (0, L) x (0, T) with (k(n))(x) (0, t) = 0, (k(n))(x) (L, t) = (1 - k(L, t))(-beta), t is an element of (0, T) and initial function k (x, 0) = k(0) (x), x is an element of[0, L] where n > 1, alpha and beta are positive constants. Second, we obtain that finite time quenching on the boundary, as well as k(t) blows up at the same finite time and a local existence result by the help of steady state of the equation k(t) = (k(n))(xx), (x, t) is an element of (0, L) x (0, T) with (k(n))(x) (0, t) = (1 - k(0, t))(-alpha), (k(n))(x) (L, t) = (1 - k(L, t))(-beta), t is an element of(0, T) and initial function k (x, 0) = k(0) (x), x is an element of [0, L] where n > 1, alpha and beta are positive constants.eninfo:eu-repo/semantics/openAccessMaximum principlesNonlinear diffusion equationHeat equationQuenchingSingular boundary conditionArticle10.5556/j.tkjm.53.2022.38532-s2.0-851050888051852Q317553WOS:000800609400006N/A