Regularity and solutions for flame modelling in porous medium
The presented article deals with a model of flame propagation in porous medium. We depart from previously reported models in flame propagation, and we propose a new modelling conception based on a p-Laplacian operator. Such an operator is intended to extend the conceptions for reproducing the diffus...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-09-01
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| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379723006447 |
| _version_ | 1797682823818117120 |
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| author | José Luis Díaz Palencia Saeed ur Rahman Julian Roa Gonzalez Abraham Otero |
| author_facet | José Luis Díaz Palencia Saeed ur Rahman Julian Roa Gonzalez Abraham Otero |
| author_sort | José Luis Díaz Palencia |
| collection | DOAJ |
| description | The presented article deals with a model of flame propagation in porous medium. We depart from previously reported models in flame propagation, and we propose a new modelling conception based on a p-Laplacian operator. Such an operator is intended to extend the conceptions for reproducing the diffusion given in porous media. In addition, we introduce a nonlinear reaction term that generalizes the classical KPP-Fisher model of typical use in combustion. Our analysis shows first the boundedness and uniqueness of weak solutions. Afterward, we reformulate the driving equations using the travelling wave technique; and we introduce a density and flux ansatz to analyse the stability of a critical point. We obtain asymptotic profiles of travelling wave solutions, by making use of the Geometric Perturbation Theory. Eventually, we obtain upper solutions under selfsimilar forms for finite support propagating flames. This is particularly applicable for flames departing from compactly supported initial pressure–temperature distributions. |
| first_indexed | 2024-03-12T00:06:25Z |
| format | Article |
| id | doaj.art-adf6bfa466df4fcbb1dbd428ff6c10df |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-03-12T00:06:25Z |
| publishDate | 2023-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-adf6bfa466df4fcbb1dbd428ff6c10df2023-09-17T04:56:29ZengElsevierResults in Physics2211-37972023-09-0152106851Regularity and solutions for flame modelling in porous mediumJosé Luis Díaz Palencia0Saeed ur Rahman1Julian Roa Gonzalez2Abraham Otero3Department of Mathematics and Education, Universidad a Distancia de Madrid, Vía de Servicio A-6, 15, 28400, Madrid, Spain; Department of Information Technology, Escuela Politecnica Superior, Universidad San Pablo-CEU, CEU Universities, Campus Monteprincipe, Boadilla del Monte, Madrid 28668, Spain; Corresponding author at: Department of Mathematics and Education, Universidad a Distancia de Madrid, Vía de Servicio A-6, 15, 28400, Madrid, Spain.Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad, 22060, PakistanDepartment of Mathematics and Education, Universidad a Distancia de Madrid, Vía de Servicio A-6, 15, 28400, Madrid, SpainDepartment of Information Technology, Escuela Politecnica Superior, Universidad San Pablo-CEU, CEU Universities, Campus Monteprincipe, Boadilla del Monte, Madrid 28668, SpainThe presented article deals with a model of flame propagation in porous medium. We depart from previously reported models in flame propagation, and we propose a new modelling conception based on a p-Laplacian operator. Such an operator is intended to extend the conceptions for reproducing the diffusion given in porous media. In addition, we introduce a nonlinear reaction term that generalizes the classical KPP-Fisher model of typical use in combustion. Our analysis shows first the boundedness and uniqueness of weak solutions. Afterward, we reformulate the driving equations using the travelling wave technique; and we introduce a density and flux ansatz to analyse the stability of a critical point. We obtain asymptotic profiles of travelling wave solutions, by making use of the Geometric Perturbation Theory. Eventually, we obtain upper solutions under selfsimilar forms for finite support propagating flames. This is particularly applicable for flames departing from compactly supported initial pressure–temperature distributions.http://www.sciencedirect.com/science/article/pii/S2211379723006447Flame propagationp-LaplacianGeneralized KPP-fisherTravelling waveGeometric perturbation theoryFinite propagation |
| spellingShingle | José Luis Díaz Palencia Saeed ur Rahman Julian Roa Gonzalez Abraham Otero Regularity and solutions for flame modelling in porous medium Results in Physics Flame propagation p-Laplacian Generalized KPP-fisher Travelling wave Geometric perturbation theory Finite propagation |
| title | Regularity and solutions for flame modelling in porous medium |
| title_full | Regularity and solutions for flame modelling in porous medium |
| title_fullStr | Regularity and solutions for flame modelling in porous medium |
| title_full_unstemmed | Regularity and solutions for flame modelling in porous medium |
| title_short | Regularity and solutions for flame modelling in porous medium |
| title_sort | regularity and solutions for flame modelling in porous medium |
| topic | Flame propagation p-Laplacian Generalized KPP-fisher Travelling wave Geometric perturbation theory Finite propagation |
| url | http://www.sciencedirect.com/science/article/pii/S2211379723006447 |
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