Non-simultaneous Blow-up in a Nonlinear Parabolic System
Abstract: We prove the existence of a nontrivially coupled parabolic system such that one of its components becomes unbounded at a finite time while the other remains bounded, a situation that we denote as non-simultaneous blow-up. Our system consists of two porous medium equations with coupled nonlinear flux boundary conditions. As a preliminary step, we will obtain a necessary and sufficient condition for blow-up. Next we characterize completely, in the case of increasing in time solutions, the set of parameters appearing in the system for which nonsimultaneous blow-up indeed occurs. In the course of our proofs we will obtain a necessary and sufficient condition for the blow-up of solutions to general porous medium type equations on the half-line with a prescribed flux at the boundary blowing up at a finite time, a result of independent interest.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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Non-simultaneous Blow-up in a Nonlinear Parabolic System ; volume:3 ; number:3 ; year:2003 ; pages:397-418 ; extent:22
Advanced nonlinear studies ; 3, Heft 3 (2003), 397-418 (gesamt 22)
- Creator
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Quirós, Fernando
Rossi, Julio D.
- DOI
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10.1515/ans-2003-0304
- URN
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urn:nbn:de:101:1-2405021623112.559276397994
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
- 14.08.2025, 11:02 AM CEST
Data provider
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Quirós, Fernando
- Rossi, Julio D.
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