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Eternal solutions to a porous medium equation with strong non-homogeneous absorption. Part I: radially non-increasing profiles
Published online by Cambridge University Press: 14 March 2024
Abstract
Existence of specific eternal solutions in exponential self-similar form to the following quasilinear diffusion equation with strong absorption, with $m>1$
, $q\in (0,\,1)$
and $\sigma =\sigma _c:=2(1-q)/ (m-1)$
is proved. Looking for radially symmetric solutions of the form
for which there exists a one-parameter family $(u_A)_{A>0}$
of solutions with compactly supported and non-increasing profiles $(f_A)_{A>0}$
satisfying $f_A(0)=A$
and $f_A'(0)=0$
. An important feature of these solutions is that they are bounded and do not vanish in finite time, a phenomenon which is known to take place for all non-negative bounded solutions when $\sigma \in (0,\,\sigma _c)$
.
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- Research Article
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- Copyright
- Copyright © The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
References
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