Analysis of travelling waves and propagating supports for a nonlinear model of flame propagation with a p-Laplacian operator and advection

Abstract In this paper, we propose a new model to characterize the behaviour of a flame driven by temperature and pressure variables. The model is formulated using a p-Laplacian operator, an advection term, and a nonlinear reaction (considering linear kinetics). First, the uniqueness and boundedness...

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Published inNonlinearity Vol. 36; no. 9; pp. 4954 - 4980
Main Authors Díaz Palencia, José Luis, Rahman, Saeed ur
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.09.2023
Subjects
35B65
35K92
35Q35
finite propagation
flame propagation
geometric perturbation theory
p-Laplacian
travelling wave
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Abstract Abstract In this paper, we propose a new model to characterize the behaviour of a flame driven by temperature and pressure variables. The model is formulated using a p-Laplacian operator, an advection term, and a nonlinear reaction (considering linear kinetics). First, the uniqueness and boundedness of the weak solutions are demonstrated. Subsequently, traveling wave solutions supported by the geometric perturbation theory are obtained. As a major outcome, minimum traveling wave speeds are shown to exist, for which the associated profiles of the solutions are purely monotonic with exponential behaviour. The assumptions considered in the analytical approach are further explored through a numerical assessment, and self-similar solutions are constructed to determine the evolution of the flame front in terms of the temperature and pressure variables.
AbstractList Abstract In this paper, we propose a new model to characterize the behaviour of a flame driven by temperature and pressure variables. The model is formulated using a p-Laplacian operator, an advection term, and a nonlinear reaction (considering linear kinetics). First, the uniqueness and boundedness of the weak solutions are demonstrated. Subsequently, traveling wave solutions supported by the geometric perturbation theory are obtained. As a major outcome, minimum traveling wave speeds are shown to exist, for which the associated profiles of the solutions are purely monotonic with exponential behaviour. The assumptions considered in the analytical approach are further explored through a numerical assessment, and self-similar solutions are constructed to determine the evolution of the flame front in terms of the temperature and pressure variables.
Author Díaz Palencia, José Luis
Rahman, Saeed ur
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Snippet Abstract In this paper, we propose a new model to characterize the behaviour of a flame driven by temperature and pressure variables. The model is formulated...
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StartPage 4954
SubjectTerms 35B65
35K92
35Q35
finite propagation
flame propagation
geometric perturbation theory
p-Laplacian
travelling wave
Title Analysis of travelling waves and propagating supports for a nonlinear model of flame propagation with a p-Laplacian operator and advection
URI https://iopscience.iop.org/article/10.1088/1361-6544/aceccd
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