6533b7d4fe1ef96bd12631db
RESEARCH PRODUCT
Existence of a traveling wave solution in a free interface problem with fractional order kinetics
Claude-michel BraunerClaude-michel BraunerRobert RoussarieLinwan ZhangPeipei Shangsubject
Settling timeScalar (mathematics)01 natural sciencesPoincare-Bendixson TheoremTraveling wave solutionsMathematics - Analysis of PDEsDimension (vector space)Free boundary problemFOS: Mathematics[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]Trapping triangles0101 mathematicsMathematicsPhase portraitApplied Mathematics010102 general mathematicsMathematical analysisIntegral equationStable manifoldDiffusional-thermal combustionFree interface problems010101 applied mathematicsVector fieldFractional order kineticsAnalysisAnalysis of PDEs (math.AP)description
Abstract In this paper we consider a system of two reaction-diffusion equations that models diffusional-thermal combustion with stepwise ignition-temperature kinetics and fractional reaction order 0 α 1 . We turn the free interface problem into a scalar free boundary problem coupled with an integral equation. The main intermediary step is to reduce the scalar problem to the study of a non-Lipschitz vector field in dimension 2. The latter is treated by qualitative topological methods based on the Poincare-Bendixson Theorem. The phase portrait is determined and the existence of a stable manifold at the origin is proved. A significant result is that the settling time to reach the origin is finite, meaning that the trailing interface is finite in contrast to the case α = 1 , but in accordance with α = 0 . Finally, the integro-differential system is solved via a fixed-point method.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-04-25 |