The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Delfim F. M. Torres - One of the best experts on this subject based on the ideXlab platform.
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Necessary Condition for an Euler-Lagrange Equation on Time Scales
Abstract and Applied Analysis, 2014Co-Authors: Monika Dryl, Delfim F. M. TorresAbstract:We prove a necessary condition for a dynamic integrodifferential Equation to be an Euler-Lagrange Equation. New and interesting results for the discrete and quantum calculus are obtained as particular cases. An example of a second order dynamic Equation, which is not an Euler-Lagrange Equation on an arbitrary time scale, is given.
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the dubois reymond fundamental lemma of the fractional calculus of variations and an Euler Lagrange Equation involving only derivatives of caputo
Journal of Optimization Theory and Applications, 2013Co-Authors: Matheus J. Lazo, Delfim F. M. TorresAbstract:Derivatives and integrals of noninteger order were introduced more than three centuries ago but only recently gained more attention due to their application on nonlocal phenomena. In this context, the Caputo derivatives are the most popular approach to fractional calculus among physicists, since differential Equations involving Caputo derivatives require regular boundary conditions. Motivated by several applications in physics and other sciences, the fractional calculus of variations is currently in fast development. However, all current formulations for the fractional variational calculus fail to give an Euler–Lagrange Equation with only Caputo derivatives. In this work, we propose a new approach to the fractional calculus of variations by generalizing the DuBois–Reymond lemma and showing how Euler–Lagrange Equations involving only Caputo derivatives can be obtained.
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Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives
Communications in Nonlinear Science and Numerical Simulation, 2011Co-Authors: Ricardo Almeida, Delfim F. M. TorresAbstract:Abstract We prove optimality conditions for different variational functionals containing left and right Caputo fractional derivatives. A sufficient condition of minimization under an appropriate convexity assumption is given. An Euler–Lagrange Equation for functionals where the lower and upper bounds of the integral are distinct of the bounds of the Caputo derivative is also proved. Then, the fractional isoperimetric problem is formulated with an integral constraint also containing Caputo derivatives. Normal and abnormal extremals are considered.
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the second Euler Lagrange Equation of variational calculus on time scales
European Journal of Control, 2011Co-Authors: Zbigniew Bartosiewicz, Natalia Martins, Delfim F. M. TorresAbstract:The fundamental problem of the calculus of variations on time scales concerns the minimization of a delta-integral over all trajectories satisfying given boundary conditions. In this paper, we prove the second Euler-Lagrange necessary optimality condition for optimal trajectories of variational problems on time scales. As an example of application of the main result, we give an alternative and simpler proof to the Noether theorem on time scales recently obtained in [J. Math. Anal. Appl. 342 (2008), no. 2, 1220–1226].
Ronald C. Davidson - One of the best experts on this subject based on the ideXlab platform.
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Field theory and weak Euler-Lagrange Equation for classical particle-field systems.
Physical Review E, 2014Co-Authors: Hong Qin, Joshua W. Burby, Ronald C. DavidsonAbstract:It is commonly believed as a fundamental principle that energy-momentum conservation of a physical system is the result of space-time symmetry. However, for classical particle-field systems, e.g., charged particles interacting through self-consistent electromagnetic or electrostatic fields, such a connection has only been cautiously suggested. It has not been formally established. The difficulty is due to the fact that the dynamics of particles and the electromagnetic fields reside on different manifolds. We show how to overcome this difficulty and establish the connection by generalizing the Euler-Lagrange Equation, the central component of a field theory, to a so-called weak form. The weak Euler-Lagrange Equation induces a new type of flux, called the weak Euler-Lagrange current, which enters conservation laws. Using field theory together with the weak Euler-Lagrange Equation developed here, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived from the underlying space-time symmetry.
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field theory and weak Euler Lagrange Equation for classical particle field systems
Physical Review E, 2014Co-Authors: Joshua W. Burby, Ronald C. DavidsonAbstract:It is commonly believed that energy-momentum conservation is the result of space-time symmetry. However, for classical particle-field systems, e.g., Klimontovich-Maxwell and Klimontovich- Poisson systems, such a connection hasn't been formally established. The difficulty is due to the fact that particles and the electromagnetic fields reside on different manifolds. To establish the connection, the standard Euler-Lagrange Equation needs to be generalized to a weak form. Using this technique, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived.
Arrigo Cellina - One of the best experts on this subject based on the ideXlab platform.
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the validity of the Euler Lagrange Equation for solutions to variational problems
Journal of Fixed Point Theory and Applications, 2014Co-Authors: Arrigo CellinaAbstract:We prove the validity of the Euler–Lagrange Equation for a class of variational problems. Mathematics Subject Classification. 49K20.
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The validity of the Euler-Lagrange Equation for solutions to variational functionals with fast growth
LIBERTAS MATHEMATICA (new series), 2013Co-Authors: Agnese Caielli, Arrigo CellinaAbstract:For L convex and dened on R N , we consider a solution u to the problem of minimizing R L(rv(x))dx. We provide a growth condition on L to guarantee that u is locally bounded and, by building suitable variations, we prove the validity of the Euler-Lagrange Equation without imposing dierentiability on L.
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The Higher Integrability and the Validity of the Euler-Lagrange Equation for Solutions to Variational Problems
SIAM Journal on Control and Optimization, 2012Co-Authors: Giovanni Bonfanti, Arrigo Cellina, Marco MazzolaAbstract:We prove higher integrability properties of solutions to the problem of minimizing $\int_{\Omega}L(x,u(x),\nabla u(x))\rm{ d}x,$ where $\xi\mapsto L(x,u,\xi)$ is a convex function satisfying some additional conditions. As an application, we prove the validity of the Euler-Lagrange Equation for a class of functionals with growth faster than exponential.
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the Euler Lagrange Equation and the pontriagin maximum principle
Bollettino Della Unione Matematica Italiana, 2005Co-Authors: Arrigo CellinaAbstract:Ω L(x, u(x),∇u(x)) dx under suitable boundary conditions. More precisely, assuming that the minimum problem admits a solution, x(·) or ũ(·),our goal is to discuss appropriate necessary conditions. a basic principle of analysis is that, given a minimum point ξ belonging to the interior of the domain of a differentiable function F (·), we obtain necessary condition exploring a neighborhood of ξ, and we obtain the condition 〈∇F (ξ), δ〉 = 0, yielding ∇F (ξ) = 0 In the same order of ideas, one considers an admissible variation, i.e., a smooth function η(·), equal to zero at the boundary, multiplies this functions by a scalar e and considers the function x+ eη. In principle, by deriving with respect to the parameter e and passing to the limit under the integral sign (this is the difficult step), one obtains the Euler Lagrange Equations (E-L): ∫ b
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On the Bounded Slope Condition and the Validity of the Euler Lagrange Equation
SIAM Journal on Control and Optimization, 2002Co-Authors: Arrigo CellinaAbstract:Under the bounded slope condition on the boundary values of a minimization problem for a functional of the gradient of u, we show that a continuous minimizer w is, in fact, Lipschitzian. An application of this result to prove the validity of the Euler Lagrange Equation for w is presented.
Nong Xiang - One of the best experts on this subject based on the ideXlab platform.
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general field theory and weak Euler Lagrange Equation for classical particle field systems in plasma physics
Physics of Plasmas, 2019Co-Authors: Jianyuan Xiao, Nong XiangAbstract:A general field theory for classical particle-field systems is developed. Compared to the standard classical field theory, the distinguishing feature of a classical particle-field system is that the particles and fields reside on different manifolds. The fields are defined on the 4D space-time, whereas each particle's trajectory is defined on the 1D time-axis. As a consequence, the standard Noether's procedure for deriving local conservation laws in space-time from symmetries is not applicable without modification. To overcome this difficulty, a weak Euler-Lagrange Equation for particles is developed on the 4D space-time, which plays a pivotal role in establishing the connections between symmetries and local conservation laws in space-time. Specifically, the nonvanishing Euler derivative in the weak Euler-Lagrange Equation generates a new current in the conservation laws. Several examples from plasma physics are studied as special cases of the general field theory. In particular, the relations between the rotational symmetry and angular momentum conservation for the Klimontovich-Poisson system and the Klimontovich-Darwin system are established.A general field theory for classical particle-field systems is developed. Compared to the standard classical field theory, the distinguishing feature of a classical particle-field system is that the particles and fields reside on different manifolds. The fields are defined on the 4D space-time, whereas each particle's trajectory is defined on the 1D time-axis. As a consequence, the standard Noether's procedure for deriving local conservation laws in space-time from symmetries is not applicable without modification. To overcome this difficulty, a weak Euler-Lagrange Equation for particles is developed on the 4D space-time, which plays a pivotal role in establishing the connections between symmetries and local conservation laws in space-time. Specifically, the nonvanishing Euler derivative in the weak Euler-Lagrange Equation generates a new current in the conservation laws. Several examples from plasma physics are studied as special cases of the general field theory. In particular, the relations between the...
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general field theory and weak Euler Lagrange Equation for classical particle field systems in plasma physics
arXiv: Plasma Physics, 2019Co-Authors: Hong Qin, Jianyuan Xiao, Peifeng Fan, Nong XiangAbstract:A general field theory for classical particle-field systems is developed. Compared with the standard classical field theory, the distinguish feature of a classical particle-field system is that the particles and fields reside on different manifolds. The fields are defined on the 4D space-time, whereas each particle's trajectory is defined on the 1D time-axis. As a consequence, the standard Noether's procedure for deriving local conservation laws in space-time from symmetries is not applicable without modification. To overcome this difficulty, a weak Euler-Lagrange Equation for particles is developed on the 4D space-time, which plays a pivotal role in establishing the connections between symmetries and local conservation laws in space-time. Especially, the non-vanishing Euler derivative in the weak Euler-Lagrangian Equation generates a new current in the conservation laws. Several examples from plasma physics are studied as special cases of the general field theory. In particular, the relations between the rotational symmetry and angular momentum conservation for the Klimontovich-Poisson system and the Klimontovich-Darwin system are established.
Joshua W. Burby - One of the best experts on this subject based on the ideXlab platform.
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Field theory and weak Euler-Lagrange Equation for classical particle-field systems.
Physical Review E, 2014Co-Authors: Hong Qin, Joshua W. Burby, Ronald C. DavidsonAbstract:It is commonly believed as a fundamental principle that energy-momentum conservation of a physical system is the result of space-time symmetry. However, for classical particle-field systems, e.g., charged particles interacting through self-consistent electromagnetic or electrostatic fields, such a connection has only been cautiously suggested. It has not been formally established. The difficulty is due to the fact that the dynamics of particles and the electromagnetic fields reside on different manifolds. We show how to overcome this difficulty and establish the connection by generalizing the Euler-Lagrange Equation, the central component of a field theory, to a so-called weak form. The weak Euler-Lagrange Equation induces a new type of flux, called the weak Euler-Lagrange current, which enters conservation laws. Using field theory together with the weak Euler-Lagrange Equation developed here, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived from the underlying space-time symmetry.
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field theory and weak Euler Lagrange Equation for classical particle field systems
Physical Review E, 2014Co-Authors: Joshua W. Burby, Ronald C. DavidsonAbstract:It is commonly believed that energy-momentum conservation is the result of space-time symmetry. However, for classical particle-field systems, e.g., Klimontovich-Maxwell and Klimontovich- Poisson systems, such a connection hasn't been formally established. The difficulty is due to the fact that particles and the electromagnetic fields reside on different manifolds. To establish the connection, the standard Euler-Lagrange Equation needs to be generalized to a weak form. Using this technique, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived.