Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 178, pp. 120.
Existence and blowup of solutions for a semilinear filtration problem
Evangelos A. Latos, Dimitrios E. Tzanetis
Abstract:
We first examine the existence and uniqueness of local solutions
to the semilinear filtration equation
,
for
,
with initial data
and appropriate boundary
conditions. Our main result is the proof of blowup of solutions
for some
.
Moreover, we discuss the existence of solutions for the corresponding
steadystate problem. It is found that there exists a critical value
such that for
the problem has no
stationary solution of any kind, while for
there exist classical stationary solutions.
Finally, our main result is that the solution for
,
blowsup in finite time independently of
.
The functions f,K are positive, increasing and convex and K'/f
is integrable at infinity.
Submitted July 14, 2013. Published August 4, 2013.
Math Subject Classifications: 35K55, 35B44, 35B51, 76S05.
Key Words: Blowup; filtration problem; existence; upper and lower solutions.
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Evangelos A. Latos
Institute for Mathematics and Scientific Computing
University of Graz
A8010 Graz, Heinrichstrasse, 36, Austria
email: evangelos.latos@unigraz.at


Dimitrios E. Tzanetis
Department of Mathematics
School of Applied Mathematical and Physical Sciences
National Technical University of Athens, Zografou Campus
157 80 Athens, Greece
email: dtzan@math.ntua.gr

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