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Journal articles on the topic 'Abstract boundary'

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Author: Grafiati

Published: 4 June 2021

Last updated: 28 January 2023

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1

Knox, Robert W. O'B. "Kaolinite influx within Paleocene/Eocene boundary strata of western Europe (Extended abstract)." Newsletters on Stratigraphy 36, no. 1 (January 15, 1998): 49–53. http://dx.doi.org/10.1127/nos/36/1998/49.

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2

Gür, H. "Relativistic Electromagnetic Boundary Conditions - Abstract." Journal of Electromagnetic Waves and Applications 13, no. 9 (January 1999): 1207–8. http://dx.doi.org/10.1163/156939399x01483.

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3

Palencia, C., and I. Alonso Mallo. "Abstract initial boundary value problems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 124, no. 5 (1994): 879–908. http://dx.doi.org/10.1017/s0308210500022393.

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We consider abstract initial boundary value problems in a spirit similar to that of the classical theory of linear semigroups. We assume that the solution u at time t is given by u(t) = S(t) ξ + V(t)g, where ξ and g are respectively the initial and boundary data and S(t) and V(t) are linear operators. We take as a departing point the functional equations satisfied by the propagators S and V. We discuss conditions under which a pair (S, V) describes the solution of an abstract differential initial boundary value problem. Several examples are provided of parabolic and hyperbolic problems that can be accommodated within the abstract theory. We study the backward Euler's method for the time integration of the problems considered.

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4

Prüss, Jan. "Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in $L_p$-spaces." Mathematica Bohemica 127, no. 2 (2002): 311–27. http://dx.doi.org/10.21136/mb.2002.134160.

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5

Whale, Ben E., Michael J. S. L. Ashley, and Susan M. Scott. "Generalizations of the abstract boundary singularity theorem." Classical and Quantum Gravity 32, no. 13 (May 28, 2015): 135001. http://dx.doi.org/10.1088/0264-9381/32/13/135001.

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6

Ashley, Michael J. S. L. "The Stability of Abstract Boundary Essential Singularities." General Relativity and Gravitation 34, no. 10 (October 2002): 1625–35. http://dx.doi.org/10.1023/a:1020168106488.

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7

Shakhmurov, Veli. "Abstract elliptic equations with integral boundary conditons." Chinese Annals of Mathematics, Series B 37, no. 4 (June 29, 2016): 625–42. http://dx.doi.org/10.1007/s11401-016-0948-6.

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8

Mugnolo, Delio. "Abstract wave equations with acoustic boundary conditions." Mathematische Nachrichten 279, no. 3 (February 2006): 299–318. http://dx.doi.org/10.1002/mana.200310362.

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9

Hillion, P. "IMPEDANCE BOUNDARY CONDITIONS ON A CHIRAL FILM - Abstract." Journal of Electromagnetic Waves and Applications 18, no. 3 (January 2004): 373–74. http://dx.doi.org/10.1163/156939304323085766.

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10

Lampart, Jonas, and Julian Schmidt. "On Nelson-Type Hamiltonians and Abstract Boundary Conditions." Communications in Mathematical Physics 367, no. 2 (February 23, 2019): 629–63. http://dx.doi.org/10.1007/s00220-019-03294-x.

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11

Bátkai, András, and Klaus-Jochen Engel. "Abstract wave equations with generalized Wentzell boundary conditions." Journal of Differential Equations 207, no. 1 (December 2004): 1–20. http://dx.doi.org/10.1016/j.jde.2003.12.005.

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12

Agarwal, Ravi P., and Donal O'Regan. "Difference equations in abstract spaces." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 64, no. 2 (April 1998): 277–84. http://dx.doi.org/10.1017/s1446788700001762.

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13

Lasiecka, I. "Galerkin Approximations of Abstract Parabolic Boundary Value Problems With Rough Boundary Data-L p Theory." Mathematics of Computation 47, no. 175 (July 1986): 55. http://dx.doi.org/10.2307/2008082.

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14

Balachandran, K., E. R. Anandhi, and J. P. Dauer. "Boundary controllability of Sobolev-type abstract nonlinear integrodifferential systems." Journal of Mathematical Analysis and Applications 277, no. 2 (January 2003): 446–64. http://dx.doi.org/10.1016/s0022-247x(02)00522-x.

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15

Voititsky, V. I., N. D. Kopachevsky, and P. A. Starkov. "Multicomponent conjugation problems and auxiliary abstract boundary-value problems." Journal of Mathematical Sciences 170, no. 2 (September 29, 2010): 131–72. http://dx.doi.org/10.1007/s10958-010-0078-8.

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16

Ivanov, D. Yu. "Inverse boundary value problems for an abstract elliptic equation." Differential Equations 36, no. 4 (April 2000): 579–86. http://dx.doi.org/10.1007/bf02754252.

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17

Lei, Peng, and Mingzhu Yang. "THE SOLVABILITY OF SEMI-ADMISSIBLE ABSTRACT BOUNDARY VALUE PROBLEM." Acta Mathematica Scientia 10, no. 1 (January 1990): 57–62. http://dx.doi.org/10.1016/s0252-9602(18)30379-5.

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18

Thabet, Sabri T. M., Bashir Ahmad, and Ravi P. Agarwal. "On abstract Hilfer fractional integrodifferential equations with boundary conditions." Arab Journal of Mathematical Sciences 26, no. 1/2 (March 14, 2019): 107–25. http://dx.doi.org/10.1016/j.ajmsc.2019.03.001.

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In this paper, we study a Cauchy-type problem for Hilfer fractional integrodifferential equations with boundary conditions. The existence of solutions for the given problem is proved by applying measure of noncompactness technique in an abstract weighted space. Moreover, we use generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of ϵ-approximate solutions.

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19

Bourlard, Maryse, and Serge Nicaise. "Abstract green formula and applications to boundary integral equations." Numerical Functional Analysis and Optimization 18, no. 7-8 (January 1997): 667–89. http://dx.doi.org/10.1080/01630569708816786.

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20

Milman, D. "The abstract linear boundary value problem (a nongroup approach)." Integral Equations and Operator Theory 9, no. 1 (January 1986): 11–30. http://dx.doi.org/10.1007/bf01257059.

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21

Hinuma, Yoyo, Masanori Kohyama, and Shingo Tanaka. "Boundary plane-oriented grain boundary model generation." Modelling and Simulation in Materials Science and Engineering 30, no. 4 (March 30, 2022): 045005. http://dx.doi.org/10.1088/1361-651x/ac58b5.

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Abstract This study proposes algorithms for building tilt grain boundary (GB) models with a boundary plane-oriented approach that does not rely on existence of a coincidence site lattice (CSL). As conventional GB model generation uses the CSL of superimposed grains as the starting point, our totally different approach allows systematic treatment of diverse grain boundary systems that was previously not possible. Candidates of a pair of GB planes for a selected rotation axis, constituting a symmetrical or asymmetrical tilt GB, are thoroughly obtained by computational search that is applicable to any crystal structure. A GB interface for feasible computational analysis would have two-dimensional (2D) periodicity shared by the 2D lattices of the two GB planes, hence surface-slab supercells (slab-and-vacuum models) with common in-plane basis vectors of the shared 2D lattice are obtained. Finally, a procedure to obtain a GB-model supercell with alternately stacking such slabs is given. Symmetry operations of each slab may be considered such that the iterated interfaces are symmetrically equivalent, which is beneficial in ab initio calculations. The proposed algorithms allow streamlined generation of GB models, both symmetric and asymmetric, with or without an exact 3D-CSL relation.

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22

Li, Canguang, Guohua Wang, Jin Cao, and Yi Cai. "A Nested Named Entity Recognition Model Based on Multi-agent Communication Mechanism (Student Abstract)." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 18 (May 18, 2021): 15823–24. http://dx.doi.org/10.1609/aaai.v35i18.17908.

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Traditional sequence tagging methods for named entity recognition (NER) face challenges when handling nested entities, where an entity is nested in another. Most previous methods for nested NER ignore the effect of entity boundary information or type information. Considering that entity boundary information and type information can be utilized to improve the performance of boundary detection, we propose a nested NER model with a multi-agent communication module. The type tagger and boundary tagger in the multi-agent communication module iteratively utilize the information from each other, which improves the boundary detection and the final performance of nested NER. Empirical experiments conducted on two nested NER datasets show the effectiveness of our model.

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23

Lyons, Jeffrey W., and Jeffrey T. Neugebauer. "Two point fractional boundary value problems with a fractional boundary condition." Fractional Calculus and Applied Analysis 21, no. 2 (April 25, 2018): 442–61. http://dx.doi.org/10.1515/fca-2018-0025.

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Abstract In this paper, we employ Krasnoseľskii’s fixed point theorem to show the existence of positive solutions to three different two point fractional boundary value problems with fractional boundary conditions. Also, nonexistence results are given.

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24

Lasiecka, I. "Galerkin approximations of abstract parabolic boundary value problems with rough boundary data―$L\sb p$ theory." Mathematics of Computation 47, no. 175 (September 1, 1986): 55. http://dx.doi.org/10.1090/s0025-5718-1986-0842123-x.

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25

Kang, Ping, Zhongli Wei, and Juanjuan Xu. "Positive solutions to fourth-order singular boundary value problems with integral boundary conditions in abstract spaces." Applied Mathematics and Computation 206, no. 1 (December 2008): 245–56. http://dx.doi.org/10.1016/j.amc.2008.09.010.

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26

Liu, Xiaoyang, Wenbo Xie, Weixing Chen, and Hao Zhang. "Effects of grain boundary and boundary inclination on hydrogen diffusion in α-iron." Journal of Materials Research 26, no. 21 (September 6, 2011): 2735–43. http://dx.doi.org/10.1557/jmr.2011.262.

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27

Yuasa, Motohiro, Takashi Amemiya, and Mamoru Mabuchi. "Enhanced grain boundary embrittlement of an Fe grain boundary segregated by hydrogen (H)." Journal of Materials Research 27, no. 12 (May 4, 2012): 1589–97. http://dx.doi.org/10.1557/jmr.2012.111.

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28

Molodov, D. A., L. S. Shvindlerman, and G. Gottstein. "Impact of grain boundary character on grain boundary kinetics." International Journal of Materials Research 94, no. 10 (October 1, 2003): 1117–26. http://dx.doi.org/10.1515/ijmr-2003-0203.

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Abstract The current research on grain boundary dynamics in metals is reviewed. The boundary dynamics, i. e., the boundary reaction to applied forces, is strongly dependent on the grain boundary character, which is commonly reduced to the orientation relationship between adjacent grains and impurity segregation at the boundary. The misorientation dependence of the motion of specific capillary driven grain boundaries, the effect of inclination on the mobility of planar boundaries and the dislocation absorption by moving boundaries are considered. The role of segregation behaviour and boundary crystallography for the orientation dependence of boundary mobility is addressed. The compensation effect for the motion of structurally different grain boundaries is discussed.

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29

Kelevedjiev, P., and N. Popivanov. "Second Order Boundary Value Problems with Nonlinear Two-Point Boundary Conditions." Georgian Mathematical Journal 7, no. 4 (December 2000): 677–88. http://dx.doi.org/10.1515/gmj.2000.677.

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Abstract The existence results obtained for the Dirichlet and mixed BVPs for the equation x ″ = f (t, x, x′) are extended to BVPs with full nonlinear conditions. The proofs are based on the theorem of Granas, Guenther and Lee, while barrier strips are used to obtain a priori bounds for solutions.

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30

Belarbi, Abdelkader, Mouffak Benchohra, and Bapurao C. Dhage. "Existence Theory for Perturbed Nonlinear Boundary Value Problems with Integral Boundary Conditions." gmj 13, no. 2 (June 2006): 215–28. http://dx.doi.org/10.1515/gmj.2006.215.

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Abstract In this paper, the existence of solutions and extremal solutions for a second order perturbed nonlinear boundary value problem with integral boundary conditions is proved under the mixed generalized Lipschitz and Carathéodory conditions.

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31

Ryzhov, Vladimir. "Weyl–Titchmarsh Function of an Abstract Boundary Value Problem, Operator Colligations, and Linear Systems with Boundary Control." Complex Analysis and Operator Theory 3, no. 1 (November 19, 2007): 289–322. http://dx.doi.org/10.1007/s11785-007-0034-x.

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32

KANDEMÄ°R, Mustafa. "NONCLASSICAL FOURTH ORDER DISCONTINUOUS BOUNDARY VALUE PROBLEM WITH ABSTRACT LINEAR FUNCTIONALS." JOURNAL OF ADVANCES IN MATHEMATICS 12, no. 11 (December 30, 2016): 6812–20. http://dx.doi.org/10.24297/jam.v12i11.1091.

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In this study, we have considered a nonstandard boundary-value problem for fourth order differential equation on two disjoint intervals The boundary conditions contains not only endpoints and but also a point interaction and abstract linear functional So our problem is nota pure differential one. We investigate such some important properties as isomorphism, Fredholmness and coerciveness with respect to the spectral parameter.

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33

WU, Hong-xing, and Sheng-hua WANG. "The Spectrum of a Transport Operator with Abstract Boundary Conditions." Acta Analysis Functionalis Applicata 15, no. 2 (2013): 109. http://dx.doi.org/10.3724/sp.j.1160.2013.00109.

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34

Csomós, Petra, Matthias Ehrhardt, and Bálint Farkas. "Operator splitting for abstract Cauchy problems with dynamical boundary conditions." Operators and Matrices, no. 3 (2021): 903–35. http://dx.doi.org/10.7153/oam-2021-15-60.

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35

Shakhmurov, Veli B., and Aida Shahmurova. "Nonlinear abstract boundary value problems modelling atmospheric dispersion of pollutants." Nonlinear Analysis: Real World Applications 11, no. 2 (April 2010): 932–51. http://dx.doi.org/10.1016/j.nonrwa.2009.01.037.

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36

Carl, S., and S. Heikkila. "On discontinuous implicit and explicit abstract impulsive boundary value problems." Nonlinear Analysis: Theory, Methods & Applications 41, no. 5-6 (August 2000): 701–23. http://dx.doi.org/10.1016/s0362-546x(98)00305-8.

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37

Engel, Klaus-Jochen, and Naoki Tanaka. "Abstract quasilinear equations of second order with Wentzell boundary conditions." Journal of Evolution Equations 4, no. 3 (September 2004): 313–32. http://dx.doi.org/10.1007/s00028-004-0150-2.

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38

Cichoń, Mieczysław, and Hussein A. H. Salem. "Second order three-point boundary value problems in abstract spaces." Acta Mathematicae Applicatae Sinica, English Series 30, no. 4 (October 2014): 1131–52. http://dx.doi.org/10.1007/s10255-014-0429-1.

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39

Maroncelli, Dan. "An abstract approach to nonlinear boundary value problems at resonance." Nonlinear Analysis and Differential Equations 2 (2014): 83–90. http://dx.doi.org/10.12988/nade.2014.421.

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40

Barry, Richard A., and Susan M. Scott. "The attached point topology of the abstract boundary for spacetime." Classical and Quantum Gravity 28, no. 16 (July 15, 2011): 165003. http://dx.doi.org/10.1088/0264-9381/28/16/165003.

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41

Arlinskii, Yury. "Abstract Boundary Conditions for Maximal Sectorial Extensions of Sectorial Operators." Mathematische Nachrichten 209, no. 1 (January 2000): 5–36. http://dx.doi.org/10.1002/(sici)1522-2616(200001)209:1<5::aid-mana5>3.0.co;2-r.

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42

Shakhmurov, Veli. "Free boundary value problems for abstract elliptic equations and applications." Chinese Annals of Mathematics, Series B 32, no. 5 (August 26, 2011): 749–70. http://dx.doi.org/10.1007/s11401-011-0667-y.

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43

Scott, Susan M., and Peter Szekeres. "The abstract boundary—a new approach to singularities of manifolds." Journal of Geometry and Physics 13, no. 3 (April 1994): 223–53. http://dx.doi.org/10.1016/0393-0440(94)90032-9.

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44

Èdel'shteîn, S. L. "Asymptotic splitting of boundary value problems for abstract differential equations." Siberian Mathematical Journal 35, no. 6 (November 1994): 1244–61. http://dx.doi.org/10.1007/bf02104725.

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45

Ogitsu, Tadashi, and Eric Schwegler. "ChemInform Abstract: The α-β Phase Boundary of Elemental Boron." ChemInform 44, no. 10 (March 5, 2013): no. http://dx.doi.org/10.1002/chin.201310012.

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46

Denche, Mohamed. "Nonlocal boundary value problem for second order abstract elliptic differential equation." Abstract and Applied Analysis 4, no. 3 (1999): 153–68. http://dx.doi.org/10.1155/s1085337599000135.

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We establish conditions that guarantee Fredholm solvability in the Banach spaceLpof nonlocal boundary value problems for elliptic abstract differential equations of the second order in an interval. Moreover, in the spaceL2we prove in addition the coercive solvability, and the completeness of root functions (eigenfunctions and associated functions). The obtained results are then applied to the study of a nonlocal boundary value problem for Laplace equation in a cylindrical domain.

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47

Burchuladze, T., and Yu Bezhuashvili. "Three-Dimensional Boundary Value Problems of Elastothermodiffusion with Mixed Boundary Conditions." gmj 4, no. 3 (June 1997): 243–58. http://dx.doi.org/10.1515/gmj.1997.243.

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Abstract We investigate the basic boundary value problems of the connected theory of elastothermodiffusion for three-dimensional domains bounded by several closed surfaces when the same boundary conditions are fulfilled on every separate boundary surface, but these conditions differ on different groups of surfaces. Using the results of papers [Kupradze, Gegelia, Basheleishvili, and Burchuladze, Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity, North-Holland Publishing Company, 1979, Russian original, 1976–Mikhlin, Multi-dimensional singular integrals and integral equations, 1962], we prove theorems on the existence and uniqueness of the classical solutions of these problems.

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48

Anders, Evan H., Adam S. Jermyn, Daniel Lecoanet, J. R. Fuentes, Lydia Korre, Benjamin P. Brown, and Jeffrey S. Oishi. "Convective Boundary Mixing Processes." Research Notes of the AAS 6, no. 2 (February 28, 2022): 41. http://dx.doi.org/10.3847/2515-5172/ac5892.

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Abstract Convective motions extend beyond the nominal boundaries of a convection zone. These motions mix fluid through multiple mechanisms collectively called “convective boundary mixing.” In this note, we discuss three distinct fluid dynamical processes: convective overshoot, entrainment, and penetrative convection. We describe the structure of a convective boundary that these processes create. To resolve discrepancies between models and observations, the stellar astrophysics community should distinguish between these processes and parameterize each of them separately in 1D evolutionary models.

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49

Rubio, R. Arturo, Sarra Haouala, and Javier LLorca. "Grain boundary strengthening of FCC polycrystals." Journal of Materials Research 34, no. 13 (March 13, 2019): 2263–74. http://dx.doi.org/10.1557/jmr.2019.58.

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50

Hintermann, Thomas. "Evolution equations with dynamic boundary conditions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 113, no. 1-2 (1989): 43–60. http://dx.doi.org/10.1017/s0308210500023945.

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SynopsisIn this paper, we study boundary problems with dynamic boundary conditions, that is, with boundary operators containing time derivatives. The equations under consideration are transformed into abstract Cauchy problems x – Cx = f and x(0) = x0. Abstract theoretical results concerning the operators C are obtained by the study of a naturally arising pseudodifferential operator. For existence and uniqueness theorems concerning solutions of parabolic and hyperbolic equations, we then apply the theory of semigroups in Banach spaces. Some examples of semilinear and quasilinear problems, to which our results apply, are given.

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