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Complete Blow Up for Parabolic System Arising in a Theory of Thermal Explosion of Porous Energetic Materials

Hill, Thomas Ian
http://rave.ohiolink.edu/etdc/view?acc_num=akron1428939894

Abstract Details

2015, Master of Science, University of Akron, Applied Mathematics.
In this work we consider a natural generalization of classical Frank-Kamenetskii theory of thermal explosion (autoignition) to single phase porous energetic materials. The resulting model consists of a system of two reaction diffusion equations with a super-linear reaction term posed in a smooth bounded domain with Dirichlet boundary conditions. This model describes the initial state of evolution of temperature and pressure fields in reactive porous media. In a framework of this model, successful autoignition is associated with a blow up of the solution for the system under consideration (here, "blow up" means that the solution becomes unbounded in finite time). We show that if blow up takes place then it is complete; that is, a solution can not be prolonged in any reasonable weak sense for any time after blow up. From a physical perspective this means that if autoignition takes place, then it occurs in the entire domain occupied by the porous material. This result is a generalization of a similar result for classical Frank-Kamenetskii model obtained in [1].
Peter Gordon, Dr. (Advisor)
Dmitry Golovaty, Dr. (Committee Member)
J. Patrick Wilber, Dr. (Committee Member)
37 p.
Mathematics
blow up, Frank-Kamenetskii theory, gelfand, parabolic system of equations, single phase porous media , porous media

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Citations

  • Hill, T. I. (2015). Complete Blow Up for Parabolic System Arising in a Theory of Thermal Explosion of Porous Energetic Materials [Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1428939894

    APA Style (7th edition)

  • Hill, Thomas. Complete Blow Up for Parabolic System Arising in a Theory of Thermal Explosion of Porous Energetic Materials. 2015. University of Akron, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1428939894.

    MLA Style (8th edition)

  • Hill, Thomas. "Complete Blow Up for Parabolic System Arising in a Theory of Thermal Explosion of Porous Energetic Materials." Master's thesis, University of Akron, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=akron1428939894

    Chicago Manual of Style (17th edition)

akron1428939894
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This open access ETD is published by University of Akron and OhioLINK.