The Experts below are selected from a list of 994056 Experts worldwide ranked by ideXlab platform
Andre Lisibach - One of the best experts on this subject based on the ideXlab platform.
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characteristic initial value Problem for spherically symmetric barotropic flow
Journal of Hyperbolic Differential Equations, 2017Co-Authors: Andre LisibachAbstract:We study the equations of motion for a barotropic fluid in spherical symmetric flow. Making use of the Riemann invariants, we consider the characteristic form of these equations. In a first part, w...
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characteristic initial value Problem for spherically symmetric barotropic flow
arXiv: Analysis of PDEs, 2016Co-Authors: Andre LisibachAbstract:We study the equations of motion for a barotropic fluid in spherical symmetric flow. Making use of the Riemann invariants we consider the characteristic form of these equations. In a first part, we show that the resulting constraint equations along characteristics can be solved globally away from the center of symmetry. In a second part, given data on two intersecting characteristics, we show existence and uniqueness of a smooth solution in a neighborhood in the future of these characteristics.
Delfim F M Torres - One of the best experts on this subject based on the ideXlab platform.
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existence and uniqueness of solution for a fractional riemann liouville initial value Problem on time scales
Journal of King Saud University - Science, 2016Co-Authors: Nadia Benkhettou, Ahmed Hammoudi, Delfim F M TorresAbstract:Abstract We introduce the concept of fractional derivative of Riemann–Liouville on time scales. Fundamental properties of the new operator are proved, as well as an existence and uniqueness result for a fractional initial value Problem on an arbitrary time scale.
John M Stewart - One of the best experts on this subject based on the ideXlab platform.
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The characteristic initial value Problem for plane symmetric spacetimes with weak regularity
Classical and Quantum Gravity, 2011Co-Authors: Philippe G. Lefloch, John M StewartAbstract:The characteristic initial value Problem for plane symmetric spacetimes with weak regularity Abstract We investigate the existence and the global causal structure of plane symmetric spacetimes with weak regularity when the matter consists of an irrotational perfect fluid with pressure equal to its mass-energy density. Our theory encompasses the class of W 1, 2 regular spacetimes whose metric coefficients have square-integrable first-order derivatives and whose curvature must be understood in the sense of distributions. We formulate the characteristic initial value Problem with data posed on two null hypersurfaces intersecting along a two-plane. Relying on Newman-Penrose's formalism and expressing our weak regularity conditions in terms of the Newman-Penrose scalars, we arrive at a fully geometrical formulation in which, along each initial hypersurface, two scalar fields describing the incoming radiation must be prescribed in L 1 and W −1, 2, respectively. To analyze the future boundary of such a spacetime and identify its global causal structure, we introduce a gauge that reduces the Einstein equations to a coupled system of wave equations and ordinary differential equations for well-chosen unknowns. We prove that, within the weak regularity class under consideration and for generic initial data, a true spacetime singularity forms in finite proper time. Our formulation is robust enough so that propagating discontinuities in the curvature or in the matter variables do not prevent us from constructing a spacetime whose curvature generically blows-up on the future boundary. Earlier work on the Problem studied here was restricted to sufficiently regular and vacuum spacetimes.
Nadia Benkhettou - One of the best experts on this subject based on the ideXlab platform.
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existence and uniqueness of solution for a fractional riemann liouville initial value Problem on time scales
Journal of King Saud University - Science, 2016Co-Authors: Nadia Benkhettou, Ahmed Hammoudi, Delfim F M TorresAbstract:Abstract We introduce the concept of fractional derivative of Riemann–Liouville on time scales. Fundamental properties of the new operator are proved, as well as an existence and uniqueness result for a fractional initial value Problem on an arbitrary time scale.
Afgan Aslanov - One of the best experts on this subject based on the ideXlab platform.
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A Singular Initial-Value Problem for Second-Order Differential Equations
Abstract and Applied Analysis, 2014Co-Authors: Afgan AslanovAbstract:We are interested in the existence of solutions to Initial-Value Problems for second-order nonlinear singular differential equations. We show that the existence of a solution can be explained in terms of a more simple Initial-Value Problem. Local existence and uniqueness of solutions are proven under conditions which are considerably weaker than previously known conditions.
