Results 1 to 10 of about 764,838 (25)
Null Surfaces, Initial Values and Evolution Operators for Spinor Fields [PDF]
J.Math.Phys. 37 (1996) 1091-1099, 1995 We analyze the initial value problem for spinor fields obeying the Dirac equation, with particular attention to the characteristic surfaces. The standard Cauchy initial value problem for first order differential equations is to construct a solution function in a neighborhood of space and time from the values of the function on a selected initial value ...
arxiv +1 more source
On Killing vectors in initial value problems for asymptotically flat space-times [PDF]
Class.Quant.Grav. 17 (2000) 4981-4990, 2000 The existence of symmetries in asymptotically flat space-times are studied from the point of view of initial value problems. General necessary and sufficient (implicit) conditions are given for the existence of Killing vector fields in the asymptotic characteristic and in the hyperboloidal initial value problem (both of them are formulated on the ...
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A generalized initial value problem for ODE's [PDF]
arXiv, 2022 This paper introduces, up to the author's knowledge, for the first time the generalized initial value problem. In this problem, given an ordinary differential equation defined in some set, the initial conditions are mapped to a subset of that domain. This generalization allows some systems to radically change their properties, in fact some obstructions
arxiv
Algebraic entropy computations for lattice equations: why initial value problems do matter [PDF]
, 2019 In this letter we show that the results of degree growth (algebraic entropy) calculations for lattice equations strongly depend on the initial value problem that one chooses. We consider two problematic types of initial value configurations, one with problems in the past light-cone, the other one causing interference in the future light-cone, and apply
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Caputo q-Fractional Initial Value Problems and a q-Analogue Mittag-Leffler Function [PDF]
, 2011 Caputo q-fractional derivatives are introduced and studied. A Caputo -type q-fractional initial value problem is solved and its solution is expressed by means of a new introduced q-Mittag-Leffler function. Some open problems about q-fractional integrals are proposed as well.
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Well-posedness for weak and strong solutions of non-homogeneous initial boundary value problems for fractional diffusion equations [PDF]
arXiv, 2020 We study the well-posedness for initial boundary value problems associated with time fractional diffusion equations with non-homogenous boundary and initial values. We consider both weak and strong solutions for the problems. For weak solutions, we introduce a new definition of solutions which allows to prove the existence of solution to the initial ...
arxiv
Initial-Value Privacy of Linear Dynamical Systems [PDF]
arXiv, 2020 This paper studies initial-value privacy problems of linear dynamical systems. We consider a standard linear time-invariant system with random process and measurement noises. For such a system, eavesdroppers having access to system output trajectories may infer the system initial states, leading to initial-value privacy risks.
arxiv
Initial-boundary value problems for nearly incompressible vector fields, and applications to the Keyfitz and Kranzer system [PDF]
, 2016 We establish existence and uniqueness results for initial boundary value problems with nearly incompressible vector fields. We then apply our results to establish well-posedness of the initial-boundary value problem for the Keyfitz and Kranzer system of conservation laws in several space dimensions.
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The generalised Dirichlet to Neumann map for moving initial-boundary value problems [PDF]
, 2006 We present an algorithm for characterising the generalised Dirichlet to Neumann map for moving initial-boundary value problems. This algorithm is derived by combining the so-called global relation, which couples the initial and boundary values of the problem, with a new method for inverting certain one-dimensional integrals. This new method is based on
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The massive Thirring system in the quarter plane [PDF]
, 2018 The unified transform method (UTM) for analyzing initial-boundary value (IBV) problems provides an important generalization of the inverse scattering transform (IST) method for analyzing initial value problems. In comparison with the IST, a major difficulty of the implementation of the UTM in general is the involvement of unknown boundary values.
arxiv +1 more source