Search results for "Equations"

showing 10 items of 955 documents

Constraining the Equation of State of Neutron Stars with Genral Relativity

2005

When a radio pulsar breakes down by virtue of magnetodipole emission, its gravitational mass decreases accordingly. If the pulsar in hosted in a binary system, this mass loss will increase the orbital period of the system. We show that this relativistic effect can be indeed observable if the NS is fast and magnetized enough and that, if observed, it will help to put tight constraints on the equation of state of ultradense matter.

Neutron stars Relativity and gravitation Thermodynamic processes conduction convection equations of state
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Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations

2011

We analyze collocation methods for nonlinear homogeneous Volterra-Hammerstein integral equations with non-Lipschitz nonlinearity. We present different kinds of existence and uniqueness of nontrivial collocation solutions and we give conditions for such existence and uniqueness in some cases. Finally we illustrate these methods with an example of a collocation problem, and we give some examples of collocation problems that do not fit in the cases studied previously.

Non-Lipschitz nonlinearityVolterra integral equationMathematics::Numerical Analysissymbols.namesakeMathematics - Analysis of PDEs45D05 45G10 65R20 34A12Computer Science::Computational Engineering Finance and ScienceCollocation methodFOS: MathematicsOrthogonal collocationNonlinear integral equationsMathematics - Numerical AnalysisUniquenessMathematicsPhysics::Computational PhysicsCollocation methodsCollocationApplied MathematicsMathematical analysisComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)Numerical Analysis (math.NA)Nontrivial solutionsIntegral equationComputer Science::Numerical AnalysisNonlinear systemComputational MathematicssymbolsLinear equationAnalysis of PDEs (math.AP)Journal of Computational and Applied Mathematics
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Diffusion Equations with Finite Speed of Propagation

2007

In this paper we summarize some of our recent results on diffusion equations with finite speed of propagation. These equations have been introduced to correct the infinite speed of propagation predicted by the classical linear diffusion theory.

Nonlinear parabolic equationsLinear diffusionPhysicsMathematical analysisFinite volume method for one-dimensional steady state diffusionDiffusion (business)
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Optimal control for state constrained two-phase Stefan problems

1991

We give a new approach to state constrained control problems associated to non-degenerate nonlinear parabolic equations of Stefan type. We obtain uniform estimates for the violation of the constraints.

Nonlinear parabolic equationsMathematical analysisMathematics::Analysis of PDEsPhase (waves)State (functional analysis)Type (model theory)Optimal controlMathematics
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QUALITATIVE PROPERTIES OF THE SOLUTIONS OF A NONLINEAR FLUX-LIMITED EQUATION ARISING IN THE TRANSPORT OF MORPHOGENS

2011

In this paper we study some qualitative properties of the solutions of a nonlinear flux-limited equation arising in the transport of morphogens in biological systems. Questions related to the existence of steady states, the finite speed of propagating fronts or the regularization in the interior of the support are studied from analytical and numerical points of view.

Nonlinear parabolic equationsNonlinear systemApplied MathematicsModeling and SimulationRegularization (physics)Mathematical analysisHeat equationMathematicsMathematical Models and Methods in Applied Sciences
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An approximate technique for determining in closed-form the response transition probability density function of diverse nonlinear/hysteretic oscillat…

2019

An approximate analytical technique is developed for determining, in closed form, the transition probability density function (PDF) of a general class of first-order stochastic differential equations (SDEs) with nonlinearities both in the drift and in the diffusion coefficients. Specifically, first, resorting to the Wiener path integral most probable path approximation and utilizing the Cauchy–Schwarz inequality yields a closed-form expression for the system response PDF, at practically zero computational cost. Next, the accuracy of this approximation is enhanced by proposing a more general PDF form with additional parameters to be determined. This is done by relying on the associated Fokke…

Nonlinear stochastic dynamics Path integral Cauchy–Schwarz inequalityFokker–Planck equationStochastic differential equationsSettore ICAR/08 - Scienza Delle Costruzioni
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A parallel splitting up method and its application to Navier-Stokes equations

1991

A parallel splitting-up method (or the so called alternating-direction method) is proposed in this paper. The method not only reduces the original linear and nonlinear problems into a series of one dimensional linear problems, but also enables us to compute all these one dimensional linear problems by parallel processors. Applications of the method to linear parabolic problem, steady state and nonsteady state Navier-Stokes problems are given. peerReviewed

Nonlinear systemAlternating direction implicit methodSteady stateSeries (mathematics)business.industryApplied MathematicsMathematical analysisParabolic problemComputational fluid dynamicsNavier–Stokes equationsbusinessFinite element methodMathematicsApplied Mathematics Letters
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Nonlinear Functional Difference Equations with Applications

2013

Nonlinear systemArticle SubjectSimultaneous equationsModeling and Simulationlcsh:MathematicsMathematical analysisFinite difference methodlcsh:QA1-939MathematicsDiscrete Dynamics in Nature and Society
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Homoclinic Solutions of Nonlinear Laplacian Difference Equations Without Ambrosetti-Rabinowitz Condition

2021

The aim of this paper is to establish the existence of at least two non-zero homoclinic solutions for a nonlinear Laplacian difference equation without using Ambrosetti-Rabinowitz type-conditions. The main tools are mountain pass theorem and Palais-Smale compactness condition involving suitable functionals.

Nonlinear systemCompact spaceSettore MAT/05 - Analisi MatematicaDifferential equationGeneral MathematicsMountain pass theoremMathematical analysisMathematics::Analysis of PDEsGeneral Physics and AstronomyHomoclinic orbitLaplace operator(p q)-Laplacian operator Difference equations homoclinic solutions non-zero solutionsMathematicsActa Mathematica Scientia
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MAST-2D diffusive model for flood prediction on domains with triangular Delaunay unstructured meshes

2011

Abstract A new methodology for the solution of the 2D diffusive shallow water equations over Delaunay unstructured triangular meshes is presented. Before developing the new algorithm, the following question is addressed: it is worth developing and using a simplified shallow water model, when well established algorithms for the solution of the complete one do exist? The governing Partial Differential Equations are discretized using a procedure similar to the linear conforming Finite Element Galerkin scheme, with a different flux formulation and a special flux treatment that requires Delaunay triangulation but entire solution monotonicity. A simple mesh adjustment is suggested, that attains t…

Nonlinear systemMathematical optimizationDiscretizationDelaunay triangulationCourant–Friedrichs–Lewy conditionshallow waters numerical methods finite element method diffusive model unstructured meshes Delaunay triangulations Voronoi cells unsteady flow backwater effect analytical solutionLinear systemApplied mathematicsGalerkin methodShallow water equationsFinite element methodWater Science and TechnologyMathematics
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