Search results for "interface problem"

showing 2 items of 2 documents

Homogenization of the wave equation in composites with imperfect interface : a memory effect

2007

Abstract In this paper we study the asymptotic behaviour of the wave equation with rapidly oscillating coefficients in a two-component composite with e-periodic imperfect inclusions. We prescribe on the interface between the two components a jump of the solution proportional to the conormal derivatives through a function of order e γ . For the different values of γ, we obtain different limit problems. In particular, for γ = 1 we have a linear memory effect in the homogenized problem.

Mathematics(all)HomogenizationHomogenization; Hyperbolic equationsApplied MathematicsGeneral MathematicsHyperbolic equations010102 general mathematicsMathematical analysisComposite numberGeometryWave equation01 natural sciencesHomogenization (chemistry)periodic homogenization; wave equation; interface problem010101 applied mathematicsJump[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]wave equationinterface problemImperfect0101 mathematics[MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]periodic homogenizationComputingMilieux_MISCELLANEOUSMathematics
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Existence of a traveling wave solution in a free interface problem with fractional order kinetics

2021

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 fin…

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)
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