Search results for "Free interface"

showing 2 items of 2 documents

On the regularity of critical and minimal sets of a free interface problem

2015

We study a free interface problem of finding the optimal energy configuration for mixtures of two conducting materials with an additional perimeter penalization of the interface. We employ the regularity theory of linear elliptic equations to study the possible opening angles of Taylor cones and to give a different proof of a partial regularity result by Fan Hua Lin [Calc Var. Partial Differential Equations, 1993].

PhysicsRegularity of minimal surfacesInterface (Java)Applied Mathematicsta111010102 general mathematicsMathematical analysisFree interfaceConical surface01 natural sciences010305 fluids & plasmasMathematics - Analysis of PDEsFree interface0103 physical sciencesFOS: MathematicsTaylor cones0101 mathematicsEnergy (signal processing)49Q10 49N60 74G40Analysis of PDEs (math.AP)
researchProduct

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)
researchProduct