Global existence and blow-up of solutions to the porous medium equation with reaction and singular coefficients
Meglioli G (2023)
Discrete and Continuous Dynamical Systems. Series A.
Zeitschriftenaufsatz
| E-Veröff. vor dem Druck | Englisch
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Einrichtung
Abstract / Bemerkung
We study global in time existence versus blow-up in finite time of solutions to the Cauchy problem for the porous medium equation with a vari-able density rho(x) and a power-like reaction term posed in the one dimensional interval (-R, R), R > 0. Here the weight function is singular at the boundary of the domain (-R, R), indeed it is such that rho(x) (R - |x|)-q as |x|-+ R, with q > 0. We show a different behavior of solutions depending on the three cases when q > 2, q = 2 and q < 2.
Stichworte
Porous medium equation;
global existence;
blow-up;
sub-supersolutions;
comparison principle;
bounded domains
Erscheinungsjahr
2023
Zeitschriftentitel
Discrete and Continuous Dynamical Systems. Series A
ISSN
1078-0947
eISSN
1553-5231
Page URI
https://pub.uni-bielefeld.de/record/2969547
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Meglioli G. Global existence and blow-up of solutions to the porous medium equation with reaction and singular coefficients . Discrete and Continuous Dynamical Systems. Series A. 2023.
Meglioli, G. (2023). Global existence and blow-up of solutions to the porous medium equation with reaction and singular coefficients . Discrete and Continuous Dynamical Systems. Series A. https://doi.org/10.3934/dcds.2023011
Meglioli, Giulia. 2023. “Global existence and blow-up of solutions to the porous medium equation with reaction and singular coefficients ”. Discrete and Continuous Dynamical Systems. Series A.
Meglioli, G. (2023). Global existence and blow-up of solutions to the porous medium equation with reaction and singular coefficients . Discrete and Continuous Dynamical Systems. Series A.
Meglioli, G., 2023. Global existence and blow-up of solutions to the porous medium equation with reaction and singular coefficients . Discrete and Continuous Dynamical Systems. Series A.
G. Meglioli, “Global existence and blow-up of solutions to the porous medium equation with reaction and singular coefficients ”, Discrete and Continuous Dynamical Systems. Series A, 2023.
Meglioli, G.: Global existence and blow-up of solutions to the porous medium equation with reaction and singular coefficients . Discrete and Continuous Dynamical Systems. Series A. (2023).
Meglioli, Giulia. “Global existence and blow-up of solutions to the porous medium equation with reaction and singular coefficients ”. Discrete and Continuous Dynamical Systems. Series A (2023).
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