Search results for "Robin boundary conditions"

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A two-phase problem with Robin conditions on the free boundary

2020

We study for the first time a two-phase free boundary problem in which the solution satisfies a Robin boundary condition. We consider the case in which the solution is continuous across the free boundary and we prove an existence and a regularity result for minimizers of the associated variational problem. Finally, in the appendix, we give an example of a class of Steiner symmetric minimizers. peerReviewed

Class (set theory)General MathematicsBoundary (topology)variaatiolaskentaRobin boundary conditionsPhase problemRobin boundary condition01 natural sciencesFree boundary problemsRegularityMathematics - Analysis of PDEsFOS: MathematicsFree boundary problemApplied mathematics0101 mathematicsMathematicsosittaisdifferentiaaliyhtälöt010102 general mathematicsFree boundary problemFree boundary problems; Regularity; Robin boundary conditions; Two-phasematemaattinen optimointi16. Peace & justiceRobin boundary condition010101 applied mathematicsTwo-phaseAnalysis of PDEs (math.AP)
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A posteriori error estimates for time-dependent reaction-diffusion problems based on the Payne-Weinberger inequality

2015

We consider evolutionary reaction-diffusion problem with mixed Dirichlet--Robin boundary conditions. For this class of problems, we derive two-sided estimates of the distance between any function in the admissible energy space and exact solution of the problem. The estimates (majorants and minorants) are explicitly computable and do not contain unknown functions or constants. Moreover, it is proved that the estimates are equivalent to the energy norm of the deviation from the exact solution.

ta113InequalityApplied Mathematicsmedia_common.quotation_subjectta111Numerical Analysis (math.NA)Parabolic partial differential equationExact solutions in general relativityevolutionary reaction-diffusion problemsNorm (mathematics)FOS: MathematicsDiscrete Mathematics and CombinatoricsA priori and a posterioriApplied mathematicsBoundary value problemMathematics - Numerical AnalysisDirichlet–Robin boundary conditionsAnalysisMathematicsmedia_common
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