@article{Ferreira2022, 
author = {Raúl Ferreira and Arturo de Pablo},
title = {A nonlinear diffusion equation with reaction localized in the half-line},
year = {2022},
journal = {Mathematics in Engineering},
volume = {4},
number = {3},
pages = {1-24},
keywords = {blow-up, grow-up, nonlinear diffusion, Fujita exponent, asymptotic behaviour},
url = {https://www.sciopen.com/article/10.3934/mine.2022024},
doi = {10.3934/mine.2022024},
abstract = {We study the behaviour of the solutions to the quasilinear heat equation with a reaction restricted to a half-line         u    t    =  (      u    m        )          x      x        +  a  (  x  )      u    p    ,   m  ,  p  >  0 and    a  (  x  )  =  1 for    x  >  0,    a  (  x  )  =  0 for    x  <  0. We first characterize the global existence exponent        p    0    =  1 and the Fujita exponent        p    c    =  m  +  2. Then we pass to study the grow-up rate in the case    p  ≤  1 and the blow-up rate for    p  >  1. In particular we show that the grow-up rate is different as for global reaction if    p  >  m or    p  =  1  ≠  m.}
}