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.
GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS TO THE POROUS MEDIUM EQUATION WITH REACTION AND SINGULAR COEFFICIENTS
G. Meglioli
2023-01-01
Abstract
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.File in questo prodotto:
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