Evangelos A. Latos, Dimitrios E. Tzanetis
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 blow-up of solutions for some . Moreover, we discuss the existence of solutions for the corresponding steady-state 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 , blows-up 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: Blow-up; filtration problem; existence; upper and lower solutions.
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| Evangelos A. Latos |
Institute for Mathematics and Scientific Computing
University of Graz
A-8010 Graz, Heinrichstrasse, 36, Austria
| Dimitrios E. Tzanetis |
Department of Mathematics
School of Applied Mathematical and Physical Sciences
National Technical University of Athens, Zografou Campus
157 80 Athens, Greece
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