Selcuk, Burhan2024-09-292024-09-2920212651-477Xhttps://doi.org/10.15672/hujms.653805https://search.trdizin.gov.tr/tr/yayin/detay/492875https://hdl.handle.net/20.500.14619/6786This paper studies the following two non-Newtonian equations with nonlinear boundary conditions. Firstly, we show that finite time blow up occurs on the boundary and we get a blow up rate and an estimate for the blow up time of the equation k(t) = (vertical bar k(x)vertical bar(r-2) k(x))(x), (x, t) is an element of (0, L) x (0,T) with k(x) (0,t) = k(alpha) (0, t), k(x) (L,t) = k(beta) (L,t), t is an element of (0, T) and initial function k (x, 0) = k(0) (x), x is an element of [0, L] where r >= 2, alpha, beta and L are positive constants. Secondly, we show that finite time blow up occurs on the boundary, and we get blow up rates and estimates for the blow up time of the equation k(t) = (vertical bar k(x)vertical bar(r-2) k(x))(x) + k(alpha), (x, t) is an element of (0, L) x (0, T) with k(x) (0,t) = 0, k(x) (L,t) = k(beta) (L,t), t is an element of (0,T) and initial function k (x, 0) = k(0) (x), x is an element of [0, L] where r >= 2, alpha, beta and L are positive constants.eninfo:eu-repo/semantics/openAccessheat equationnonlinear parabolic equationblow upmaximum principlesArticle10.15672/hujms.6538052-s2.0-851054682835482Q354149287550WOS:000640069900021Q3