Search results for "Separable partial differential equation"

showing 7 items of 7 documents

Multiplicity results for a class of asymmetric weakly coupled systems of second order ordinary differential equations

2005

We prove the existence and multiplicity of solutions to a two-point boundary value problem associated to a weakly coupled system of asymmetric second-order equations. Applying a classical change of variables, we transform the initial problem into an equivalent problem whose solutions can be characterized by their nodal properties. The proof is developed in the framework of the shooting methods and it is based on some estimates on the rotation numbers associated to each component of the solutions to the equivalent system.

Algebra and Number TheoryMathematical analysislcsh:QA299.6-433lcsh:AnalysisExponential integratorStochastic partial differential equationLinear differential equationCollocation methodOrdinary differential equationmultiplicity result asymmetric weakly coupled system nodal solutions rotation numberBoundary value problemAnalysisMathematicsSeparable partial differential equationNumerical partial differential equations
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Regularity of solutions to differential equations with non-Lipschitz coefficients

2008

AbstractWe study the ordinary and stochastic differential equations whose coefficients satisfy certain non-Lipschitz conditions, namely, we study the behaviors of small subsets under the flows generated by these equations.

Mathematics(all)Hölder continuousGeneral MathematicsMathematical analysisHausdorff dimensionNon-Lipschitz conditionMethod of undetermined coefficientsExamples of differential equationsStochastic partial differential equationDifferential equationCollocation methodC0-semigroupDifferential algebraic equationMathematicsSeparable partial differential equationNumerical partial differential equationsBulletin des Sciences Mathématiques
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A Noncommutative Approach to Ordinary Differential Equations

2005

We adapt ideas coming from Quantum Mechanics to develop a non-commutative strategy for the analysis of some systems of ordinary differential equations. We show that the solution of such a system can be described by an unbounded, self-adjoint and densely defined operator H which we call, in analogy with Quantum Mechanics, the Hamiltonian of the system. We discuss the role of H in the analysis of the integrals of motion of the system. Finally, we apply this approach to several examples.

Pure mathematicsPhysics and Astronomy (miscellaneous)General MathematicsIntegrating factorExamples of differential equationsStochastic partial differential equationMethod of quantum characteristicsQuantum evolutionQuantum statistical mechanicsC0-semigroupDifferential algebraic equationSettore MAT/07 - Fisica MatematicaOrdinary differential equationSeparable partial differential equationMathematicsInternational Journal of Theoretical Physics
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New solvability conditions for the Neumann problem for ordinary singular differential equations

2000

Singular solutionGeneral MathematicsOrdinary differential equationMathematical analysisNeumann boundary conditionExact differential equationDifferential algebraic equationAnalysisMathematicsSeparable partial differential equationNeumann seriesIntegrating factorDifferential Equations
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Mean-field games and two-point boundary value problems

2014

A large population of agents seeking to regulate their state to values characterized by a low density is considered. The problem is posed as a mean-field game, for which solutions depend on two partial differential equations, namely the Hamilton-Jacobi-Bellman equation and the Fokker-Plank-Kolmogorov equation. The case in which the distribution of agents is a sum of polynomials and the value function is quadratic is considered. It is shown that a set of ordinary differential equations, with two-point boundary value conditions, can be solved in place of the more complicated partial differential equations associated with the problem. The theory is illustrated by a numerical example.

Stochastic partial differential equationDifferential equationMathematical analysisFree boundary problemFirst-order partial differential equationBoundary value problemHyperbolic partial differential equationNumerical partial differential equationsSeparable partial differential equationMathematics53rd IEEE Conference on Decision and Control
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Global integrability of the gradients of solutions to partial differential equations

1994

Stochastic partial differential equationMethod of characteristicsElliptic partial differential equationDifferential equationApplied MathematicsMathematical analysisFirst-order partial differential equationHyperbolic partial differential equationAnalysisMathematicsNumerical partial differential equationsSeparable partial differential equationNonlinear Analysis: Theory, Methods & Applications
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On ordinary differential equations with interface conditions

1968

Stochastic partial differential equationOscillation theoryExamples of differential equationsApplied MathematicsCollocation methodMathematical analysisDifferential algebraic equationAnalysisSeparable partial differential equationNumerical partial differential equationsMathematicsIntegrating factorJournal of Differential Equations
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