Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 67, pp. 1-19.

Title: Global solution for coupled parabolic systems with degenerate coefficients and time-weighted sources

Authors: Ricardo Castillo (Univ. del Bio-Bio, Concepcion, Chile)
         Omar Guzman-Rea (Univ.d Tecnologica de Peru, Ica, Peru)
         Miguel Loayza (Univ. Federal de Pernambuco, Brazil)
         Maria Zegarra (Univ. Nacional Mayor de San Marcos, Lima Peru)

Abstract: 
In this article we obtained the so-called Fujita exponent for the 
degenerate parabolic coupled system 
$$\displaylines{ 
u_t- \hbox{div} (\omega(x)\nabla u)= t^r v^p \cr
v_t- \hbox{div} (\omega(x)\nabla v)= t^s u^p
}$$
in  $R^N \times (0,T)$ with initial data belonging to 
$ [ L^\infty(R^N)]^2$, where $p,q > 0$ with $ pq > 1$; $r,s>-1 $, 
and either $\omega(x) = | x_1|^a$ or $\omega(x) = | x |^b$ with 
$a,b > 0$.

Submitted April 11, 2024. Published October 31, 2024.
Math Subject Classifications: 35K05, 35A01, 35K58, 35K65, 35B33.
Key Words: Global solution for coupled parabolic systems with degenerate coefficients and time-weighted sources.