Search results for "discontinuous function"

showing 3 items of 3 documents

On Regulated Solutions of Impulsive Differential Equations with Variable Times

2020

In this paper we investigate the unified theory for solutions of differential equations without impulses and with impulses, even at variable times, allowing the presence of beating phenomena, in the space of regulated functions. One of the aims of the paper is to give sufficient conditions to ensure that a regulated solution of an impulsive problem is globally defined.

Regulated functionDifferential equationlcsh:MathematicsGeneral Mathematics010102 general mathematicsMathematical analysisSolution set02 engineering and technologyimpulsive problem with variable timeslcsh:QA1-939Space (mathematics)01 natural sciencessolution setregulated functionregulated function solution set discontinuous function impulsive problem with variable timesSettore MAT/05 - Analisi Matematicadiscontinuous function0202 electrical engineering electronic engineering information engineeringComputer Science (miscellaneous)020201 artificial intelligence & image processing0101 mathematicsUnified field theoryEngineering (miscellaneous)MathematicsVariable (mathematics)Mathematics
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On a step method and a propagation of discontinuity

2019

In this paper we analyze how to compute discontinuous solutions for functional differential equations, looking at an approach which allows to study simultaneously continuous and discontinuous solutions. We focus our attention on the integral representation of solutions and we justify the applicability of such an approach. In particular, we improve the step method in such a way to solve a problem of vanishing discontinuity points. Our solutions are considered as regulated functions.

Regulated functionIntegral representationregulated function discontinuous function retarded differential equation delay Kurzweil-Stieltjes integral breaking pointsDifferential equationComputer scienceApplied Mathematics010102 general mathematicsMathematicsofComputing_NUMERICALANALYSIS01 natural sciences010101 applied mathematicsComputational MathematicsDiscontinuity (linguistics)Settore MAT/05 - Analisi MatematicaApplied mathematics0101 mathematicsFocus (optics)Step methodComputational and Applied Mathematics
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Relaxation of a weakly discontinuous functional depending on one control function

2008

The paper considers an optimal control problem of the typewhere the set M of admissible controls consists of all measurable vector‐functions h, which can take only two values h1 or h2. It is shown that the relaxation of this problem can be explicitly computed by rank‐one laminates.

weakly discontinuous functionalMathematical analysisType (model theory)Optimal controlControl functionSet (abstract data type)elliptic systemoptimal controlrelaxationControl theoryModeling and SimulationQA1-939Relaxation (approximation)AnalysisMathematicsMathematicsMathematical Modelling and Analysis
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