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Books on the topic 'Nonlocal equations in time'

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Published: 15 March 2025

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1

E, Zorumski William, and Langley Research Center, eds. Periodic time-domain nonlocal nonreflecting boundary conditions for duct acoustics. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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2

E, Zorumski William, and Langley Research Center, eds. Periodic time-domain nonlocal nonreflecting boundary conditions for duct acoustics. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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3

E, Zorumski William, and Langley Research Center, eds. Periodic time-domain nonlocal nonreflecting boundary conditions for duct acoustics. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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4

Andreu-Vaillo, Fuensanta. Nonlocal diffusion problems. Providence, R.I: American Mathematical Society, 2010.

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5

Shishmarev, I. A. (Ilʹi͡a︡ Andreevich)., ed. Nonlinear nonlocal equations in the theory of waves. Providence, R.I: American Mathematical Society, 1994.

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6

Naumkin, P. I. Nonlinear nonlocal equations in the theory of waves. Providence, R.I: American Mathematical Society, 1994.

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7

Roquejoffre, Jean-Michel. The Dynamics of Front Propagation in Nonlocal Reaction–Diffusion Equations. Cham: Springer Nature Switzerland, 2024. https://doi.org/10.1007/978-3-031-77772-1.

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8

1958-, Biler Piotr, Karch Grzegorz, and Nadzieja Tadeusz 1951-, eds. Nonlocal elliptic and parabolic problems: Proceedings of the conference held at Będlewo , September 12-15, 2003. Warszawa: Institute of Mathematics, Polish Academy of Sciences, 2004.

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9

Kamenskiĭ, G. A. Extrema of nonlocal functionals and boundary value problems for functional differential equations. Hauppauge, N.Y: Nova Science Publishers, 2007.

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10

Kubica, Adam, Katarzyna Ryszewska, and Masahiro Yamamoto. Time-Fractional Differential Equations. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-9066-5.

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11

E, Zorumski W., Watson Willie R, and Langley Research Center, eds. Solution of the three-dimensional Helmholtz equation with nonlocal boundary conditions. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1995.

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12

E, Zorumski W., Watson Willie R, and Langley Research Center, eds. Solution of the three-dimensional Helmholtz equation with nonlocal boundary conditions. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1995.

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13

Georgiev, Svetlin G. Integral Equations on Time Scales. Paris: Atlantis Press, 2016. http://dx.doi.org/10.2991/978-94-6239-228-1.

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14

Bohner, Martin, and Allan Peterson. Dynamic Equations on Time Scales. Boston, MA: Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0201-1.

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15

Wang, Gengsheng, Lijuan Wang, Yashan Xu, and Yubiao Zhang. Time Optimal Control of Evolution Equations. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95363-2.

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16

Georgiev, Svetlin G. Functional Dynamic Equations on Time Scales. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-15420-2.

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17

1953-, Rao S. M., ed. Time domain electromagnetics. San Diego: Academic Press, 1999.

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18

Pötter, Ulrich. Models for interdependent decisions over time. Colchester: European Science Foundation, Scientific Network on Household Panel Studies, University of Essex, 1992.

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19

Center, Langley Research, and Institute for Computer Applications in Science and Engineering., eds. Spectral methods in time for parabolic problems. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1985.

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20

Bertil, Gustafsson. Time dependent problems and difference methods. New York: Wiley, 1995.

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21

Farina, Alberto, and Jean-Claude Saut, eds. Stationary and Time Dependent Gross-Pitaevskii Equations. Providence, Rhode Island: American Mathematical Society, 2008. http://dx.doi.org/10.1090/conm/473.

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22

Bohner, Martin, and Allan Peterson, eds. Advances in Dynamic Equations on Time Scales. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-0-8176-8230-9.

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23

Andersson, Ulf. Time-domain methods for the Maxwell equations. Stockholm: Tekniska ho gsk., 2001.

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24

1966-, Bohner Martin, and Peterson Allan C, eds. Advances in dynamic equations on time scales. Boston: Birkhäuser, 2003.

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25

name, No. Advances in dynamic equations on time scales. Boston, MA: Birkhuser, 2003.

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26

Pyke, Randall Mitchell. Time periodic solutions of nonlinear wave equations. Toronto: [s.n.], 1996.

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27

Agarwal, Ravi P., Bipan Hazarika, and Sanket Tikare. Dynamic Equations on Time Scales and Applications. Boca Raton: Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9781003467908.

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28

Gustafsson, Bertil. Time dependent problems and difference methods. New York: Wiley, 1995.

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29

Martynyuk, Anatoly A. Stability Theory for Dynamic Equations on Time Scales. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-42213-8.

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30

Gal, Ciprian G., and Mahamadi Warma. Fractional-in-Time Semilinear Parabolic Equations and Applications. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-45043-4.

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31

Kirsch, Andreas, and Frank Hettlich. The Mathematical Theory of Time-Harmonic Maxwell's Equations. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-11086-8.

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32

Sayas, Francisco-Javier. Retarded Potentials and Time Domain Boundary Integral Equations. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-26645-9.

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33

S, Liou M., Povinelli Louis A, and United States. National Aeronautics and Space Administration., eds. Multigrid time-accurate integration of Navier-Stokes equations. [Washington, DC]: National Aeronautics and Space Administration, 1993.

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34

E, Turkel, and United States. National Aeronautics and Space Administration, eds. Pseudo-time algorithms for the Navier-Stokes equations. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1986.

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35

E, Turkel, and United States. National Aeronautics and Space Administration, eds. Pseudo-time algorithms for the Navier-Stokes equations. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1986.

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36

S, Liou M., Povinelli Louis A, and United States. National Aeronautics and Space Administration., eds. Multigrid time-accurate integration of Navier-Stokes equations. [Washington, DC]: National Aeronautics and Space Administration, 1993.

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37

S, Liou M., Povinelli Louis A, and United States. National Aeronautics and Space Administration., eds. Multigrid time-accurate integration of Navier-Stokes equations. [Washington, DC]: National Aeronautics and Space Administration, 1993.

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38

Swanson, R. Charles. Pseudo-time algorithms for the Navier-Stokes equations. Hampton, Va: ICASE, 1986.

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39

Periodic time-domain nonlocal nonreflecting boundary conditions for duct acoustics. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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40

Morawetz, Klaus. Nonlocal Collision Integral. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.003.0013.

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The kinetic equation with the nonlocal shifts is presented as the final result on the way to derive the kinetic equation with nonlocal corrections. The exclusive dependence of the nonlocal and non-instant corrections on the scattering phase shift confirms the results from the theory of gases. With the approximation on the level of the Brueckner reaction matrix, the corresponding non-instant and nonlocal scattering integral in parallel with the classical Enskog’s equation, can be treated with Monte-Carlo simulation techniques. Neglecting the shifts, the Landau theory of quasiparticle transport appears. In this sense the presented kinetic theory unifies both approaches. An intrinsic symmetry is found from the optical theorem which allows for representing the collision integral equivalently either in particle-hole symmetric or space-time symmetric form.
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41

Morawetz, Klaus. Nonequilibrium Quantum Hydrodynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.003.0015.

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The balance equations resulting from the nonlocal kinetic equation are derived. They show besides the Landau-like quasiparticle contributions explicit two-particle correlated parts which can be interpreted as molecular contributions. It looks like as if two particles form a short-living molecule. All observables like density, momentum and energy are found as a conserving system of balance equations where the correlated parts are in agreement with the forms obtained when calculating the reduced density matrix with the extended quasiparticle functional. Therefore the nonlocal kinetic equation for the quasiparticle distribution forms a consistent theory. The entropy is shown to consist also of a quasiparticle part and a correlated part. The explicit entropy gain is proved to complete the H-theorem even for nonlocal collision events. The limit of Landau theory is explored when neglecting the delay time. The rearrangement energy is found to mediate between the spectral quasiparticle energy and the Landau variational quasiparticle energy.
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42

Morawetz, Klaus. Properties of Non-Instant and Nonlocal Corrections. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.003.0014.

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The derived nonlocal and non-instant shifts are discussed with respect to various symmetries and gauges. The classical counterparts are derived and found in agreement with the expected phenomenological ones from chapter 3. The explicit forms of the hard-sphere like offsets and the delay time in terms of the scattering phase shifts are calculated and discussed on the example of nuclear collision. The numerical results reveal an interesting inside into the microscopic correlations developed in dependence on the scattering angle and scattering energy. The just-accomplished derivation of the nonlocal scattering integrals is far from being intuitive. We have reached our task, the kinetic equation, being guided by nothing but systematic implementation of the quasiclassical approximation and the limit of small scattering rates.
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43

Morawetz, Klaus. Simulations of Heavy-Ion Reactions with Nonlocal Collisions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.003.0023.

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The scenario of heavy-ion reactions around the Fermi energy is explored. The quantum BUU equation is solved numerically with and without nonlocal corrections and the effect of nonlocal corrections on experimental values is calculated. A practical recipe is presented which allows reproducing the correct asymptotes of scattering by acting on the point of closest approach. The better description of dynamical correlations by the nonlocal kinetic equation is demonstrated by an enhancement of the high-energy part of the particle spectra and the enhancement of mid-rapidity charge distributions. The time-resolved solution shows the enhancement of neck formation. It is shown that the dissipated energy increases due to the nonlocal collision scenario which is responsible for the observed effects and not due to the enhancement of collisions. As final result, a method is presented how to incorporate the effective mass and quasiparticle renormalisation with the help of the nonlocal simulation scenario.
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44

Horing, Norman J. Morgenstern. Interacting Electron–Hole–Phonon System. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0011.

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Chapter 11 employs variational differential techniques and the Schwinger Action Principle to derive coupled-field Green’s function equations for a multi-component system, modeled as an interacting electron-hole-phonon system. The coupled Fermion Green’s function equations involve five interactions (electron-electron, hole-hole, electron-hole, electron-phonon, and hole-phonon). Starting with quantum Hamilton equations of motion for the various electron/hole creation/annihilation operators and their nonequilibrium average/expectation values, variational differentiation with respect to particle sources leads to a chain of coupled Green’s function equations involving differing species of Green’s functions. For example, the 1-electron Green’s function equation is coupled to the 2-electron Green’s function (as earlier), also to the 1-electron/1-hole Green’s function, and to the Green’s function for 1-electron propagation influenced by a nontrivial phonon field. Similar remarks apply to the 1-hole Green’s function equation, and all others. Higher order Green’s function equations are derived by further variational differentiation with respect to sources, yielding additional couplings. Chapter 11 also introduces the 1-phonon Green’s function, emphasizing the role of electron coupling in phonon propagation, leading to dynamic, nonlocal electron screening of the phonon spectrum and hybridization of the ion and electron plasmons, a Bohm-Staver phonon mode, and the Kohn anomaly. Furthermore, the single-electron Green’s function with only phonon coupling can be rewritten, as usual, coupled to the 2-electron Green’s function with an effective time-dependent electron-electron interaction potential mediated by the 1-phonon Green’s function, leading to the polaron as an electron propagating jointly with its induced lattice polarization. An alternative formulation of the coupled Green’s function equations for the electron-hole-phonon model is applied in the development of a generalized shielded potential approximation, analysing its inverse dielectric screening response function and associated hybridized collective modes. A brief discussion of the (theoretical) origin of the exciton-plasmon interaction follows.
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45

Nonlocal diffusion problems. Providence, R.I: American Mathematical Society, 2010.

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46

Nonlocal and abstract parabolic equations and their applications. Warszawa: Institute of Mathematics, Polish Academy of Sciences, 2009.

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47

Delay Differential Evolutions Subjected to Nonlocal Initial Conditions. Taylor & Francis Group, 2018.

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48

Necula, Mihai, Ioan I. Vrabie, Monica-Dana Burlică, and Daniela Roșu. Delay Differential Evolutions Subjected to Nonlocal Initial Conditions. Taylor & Francis Group, 2018.

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49

Necula, Mihai, Ioan I. Vrabie, Monica-Dana Burlică, and Daniela Roșu. Delay Differential Evolutions Subjected to Nonlocal Initial Conditions. Taylor & Francis Group, 2018.

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50

Necula, Mihai, Ioan I. Vrabie, Monica-Dana Burlică, and Daniela Roșu. Delay Differential Evolutions Subjected to Nonlocal Initial Conditions. Taylor & Francis Group, 2016.

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