Electron. J. Differential Equations, Vol. 2024 (2024), No. 67, pp. 1-19.
Global solution for coupled parabolic systems with degenerate coefficients and time-weighted sources
Ricardo Castillo, Omar Guzman-Rea, Miguel Loayza, Maria Zegarra
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.
DOI: 10.58997/ejde.2024.67
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Ricardo Castillo
Departamento de Matemática
Facultad de Ciencias
Universidad del Bío-Bío
Avenida Collao 1202, Casilla 5-C
Concepción, Bío-Bío, Chile
email: rcastillo@ubiobio.cl
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Omar Guzmán-Rea
Universidad Tecnológica de Perú, Ica, Peru
email: c29064@utp.edu.pe
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Miguel Loayza
Departamento de Matemática
Universidade Federal de Pernambuco
Av. Jornalista Aníbal Fernandes
Cidade Universitáa
Recife, Pernambuco, Brasil
email: miguel.loayza@ufpe.br
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María Zegarra
Departamento de Matemática
Universidad Nacional Mayor de San Marcos
Av. Venezuela cuadra 34
Lima 1, Lima, Perú
email: mzegarrag@unmsm.edu.pe
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