Combustion Model in a Multilayer Porous Medium

Quasi-Linear Problem

Authors

  • Alysson T. R. da Cunha UFG
  • Jesus C. da Mota UFG
  • Ronaldo A. dos Santos UFG
  • Marcos R. Batista IFG

Abstract

Combustion processes in porous media occur in many important applications, such as in-situ oil reservoirs and biogas production in sanitary landfills. In oil recovery, the porous medium where combustion takes place consists of layers with different physical properties. Understanding how temperature changes during and after the combustion process is important for making decisions about the oil recovery process. We analyze a one-dimensional reaction-diffusion-convection model, in which temperature and gas concentration are the unknowns in the layers. [...]

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References

E. A. Alarcon, M. R. Batista, A. Cunha, J. C. Da Mota, and R. A. Santos. “Application of the semigroup theory to a combustion problem in a multi-layer porous medium”. In: Journal of Applied Analysis and Computation 13.6 (2023). doi: 10.11948/20220333.

M. R. Batista, A. Cunha, J. C. Da Mota, and R. A. Santos. “Well-posed problem for a combustion model in a multilayer porous medium”. In: Communications in Nonlinear Science and Numerical Simulation (2024), p. 108475. doi: 10.1016/j.cnsns.2024. 108475.

M. R. Batista and J. C. Da Mota. “Monotone iterative method of upper and lower solutions applied to a multilayer combustion model in porous media”. In: Nonlinear Analysis: Real World Applications 58 (2021), p. 103223. doi: 10.1016/j.nonrwa.2020.103223.

M. R. Batista, J. C. Da Mota, and R. A. Santos. “Classical solution for a nonlinear hybrid system modeling combustion in a multilayer porous medium”. In: Nonlinear Analysis: Real World Applications 63 (2022), p. 103406. doi: 10.1016/j.nonrwa.2021.103406.

J. C. Da Mota, M. M. Santos, and R. A. Santos. “The Cauchy problem for a combustion model in a porous medium with two layers”. In: Monatshefte fur Mathematik 188 (2019), pp. 131–162. doi: 10.1007/s00605-017-1114-2.

J. C. Da Mota and S. Schecter. “Combustion fronts in a porous medium with two layers”. In: Journal of Dynamics and Differential Equations 18.3 (2006), pp. 615–665. doi: 10.1007/s10884-006-9019-0.

J. C. Da Mota and M. M. Santos. “An application of the monotone iterative method to a combustion problem in porous media”. In: Nonlinear Analysis: Real World Applications 12.2 (2011), pp. 1192–1201. doi: 10.1016/j.nonrwa.2010.09.012.

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Published

2026-02-13