@article{Alazman2023, 
author = {Ibtehal Alazman and Ibtisam Aldawish and Mohamed Jleli and Bessem Samet},
title = {A higher order evolution inequality with a gradient term in the exterior of the half-ball},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {4},
pages = {9230-9246},
keywords = {evolution inequality, convection term, half-ball, critical exponent},
url = {https://www.sciopen.com/article/10.3934/math.2023463},
doi = {10.3934/math.2023463},
abstract = {We study the existence and nonexistence of weak solutions to a semilinear higher order (in time) evolution inequality involving a convection term in the exterior of the half-ball, under Dirichlet-type boundary conditions. A weight function of the form        |    x            |        a   is allowed in front of the power nonlinearity. When    a  >  −  2, we show that the dividing line with respect to existence or nonexistence is given by a critical exponent (Fujita critical exponent), which depends on the parameters of the problem, but independent of the order of the time-derivative. Our study yields naturally optimal nonexistence results for the corresponding stationary problem.}
}