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Journal articles on the topic 'Dirichlet conditions'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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1

Guo, Bao Zhu. "Further results for a one-dimensional linear thermoelastic equation with Dirichlet-Dirichlet boundary conditions." ANZIAM Journal 43, no. 3 (January 2002): 449–62. http://dx.doi.org/10.1017/s1446181100012621.

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AbstractWe show that a sequence of generalized eigenfunctions of a one-dimensional linear thermoelastic system with Dirichiet-Dirichlet boundary conditions forms a Riesz basis for the state Hilbert space. This develops a parallel result for the same system with Dirichlet-Neumann or Neumann-Dirichlet boundary conditions.

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2

Altmann, Robert. "Moving Dirichlet boundary conditions." ESAIM: Mathematical Modelling and Numerical Analysis 48, no. 6 (October 10, 2014): 1859–76. http://dx.doi.org/10.1051/m2an/2014022.

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3

de Rham, Claudia. "Massive gravity from Dirichlet boundary conditions." Physics Letters B 688, no. 2-3 (May 2010): 137–41. http://dx.doi.org/10.1016/j.physletb.2010.04.005.

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4

Arendt, W., and C. J. K. Batty. "Absorption semigroups and dirichlet boundary conditions." Mathematische Annalen 295, no. 1 (January 1993): 427–48. http://dx.doi.org/10.1007/bf01444895.

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5

Liskevich, V. A., and Yu A. Semenov. "Self-adjointness conditions for Dirichlet operators." Ukrainian Mathematical Journal 42, no. 2 (February 1990): 253–57. http://dx.doi.org/10.1007/bf01071027.

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6

D'Yakonov, E. "The dirichlet boundary conditions and related natural boundary conditions in strengthened sobolev spaces for discretized parabolic problems." Discrete Dynamics in Nature and Society 4, no. 4 (2000): 269–81. http://dx.doi.org/10.1155/s102602260000025x.

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Correctness of initial boundary value problems and their discretizations are analyzed under unusual second-order boundary conditions, which can be considered as natural boundary conditions in strengthened Sobolev spaces and as improvements (in some cases) of the classical Dirichlet boundary conditions. Special attention is paid to optimal perturbation estimates for new variants of the penalty method with respect to the Dirichlet conditions.

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7

Dudko, Anastasia, and Vyacheslav Pivovarchik. "Three spectra problem for Stieltjes string equation and Neumann conditions." Proceedings of the International Geometry Center 12, no. 1 (February 28, 2019): 41–55. http://dx.doi.org/10.15673/tmgc.v12i1.1367.

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Spectral problems are considered which appear in description of small transversal vibrations of Stieltjes strings. It is shown that the eigenvalues of the Neumann-Neumann problem, i.e. the problem with the Neumann conditions at both ends of the string interlace with the union of the spectra of the Neumann-Dirichlet problems, i.e. problems with the Neumann condition at one end and Dirichlet condition at the other end on two parts of the string. It is shown that the spectrum of Neumann-Neumann problem on the whole string, the spectrum of Neumann-Dirichlet problem on the left part of the string, all but one eigenvalues of the Neumann-Dirichlet problem on the right part of the string and total masses of the parts uniquely determine the masses and the intervals between them.

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8

Djida, Jean-Daniel, and Arran Fernandez. "Interior Regularity Estimates for a Degenerate Elliptic Equation with Mixed Boundary Conditions." Axioms 7, no. 3 (September 1, 2018): 65. http://dx.doi.org/10.3390/axioms7030065.

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The Marchaud fractional derivative can be obtained as a Dirichlet-to–Neumann map via an extension problem to the upper half space. In this paper we prove interior Schauder regularity estimates for a degenerate elliptic equation with mixed Dirichlet–Neumann boundary conditions. The degenerate elliptic equation arises from the Bernardis–Reyes–Stinga–Torrea extension of the Dirichlet problem for the Marchaud fractional derivative.

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9

Hlaváček, Ivan. "Penalty method and extrapolation for axisymmetric elliptic problems with Dirichlet boundary conditions." Applications of Mathematics 35, no. 5 (1990): 405–17. http://dx.doi.org/10.21136/am.1990.104420.

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10

Cao, Shunhua, and Stewart Greenhalgh. "Attenuating boundary conditions for numerical modeling of acoustic wave propagation." GEOPHYSICS 63, no. 1 (January 1998): 231–43. http://dx.doi.org/10.1190/1.1444317.

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Four types of boundary conditions: Dirichlet, Neumann, transmitting, and modified transmitting, are derived by combining the damped wave equation with corresponding boundary conditions. The Dirichlet attenuating boundary condition is the easiest to implement. For an appropriate choice of attenuation parameter, it can achieve a boundary reflection coefficient of a few percent in a one‐wavelength wide zone. The Neumann‐attenuating boundary condition has characteristics similar to the Dirichlet attenuating boundary condition, but it is numerically more difficult to implement. Both the transmitting boundary condition and the modified transmitting boundary condition need an absorbing boundary condition at the termination of the attenuating region. The modified transmitting boundary condition is the most effective in the suppression of boundary reflections. For multidimensional modeling, there is no perfect absorbing boundary condition, and an approximate absorbing boundary condition is used.

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11

Wubneh, Kahsay Godifey. "Solving Fundamental Solution of Non-Homogeneous Heat Equation with Dirichlet Boundary Conditions." Bulletin of Mathematical Sciences and Applications 22 (October 2020): 1–9. http://dx.doi.org/10.18052/www.scipress.com/bmsa.22.1.

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In this study, we developed a solution of nonhomogeneous heat equation with Dirichlet boundary conditions. moreover, the non-homogeneous heat equation with constant coefficient. since heat equation has a simple form, we would like to start from the heat equation to find the exact solution of the partial differential equation with constant coefficient. to emphasize our main results, we also consider some important way of solving of partial differential equation specially solving heat equation with Dirichlet boundary conditions. the main results of our paper are quite general in nature and yield some interesting solution of non-homogeneous heat equation with Dirichlet boundary conditions and it is used for problems of mathematical modeling and mathematical physics.

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12

Binz, Tim, and Klaus-Jochen Engel. "First-order evolution equations with dynamic boundary conditions." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2185 (October 19, 2020): 20190615. http://dx.doi.org/10.1098/rsta.2019.0615.

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In this paper, we introduce a general framework to study linear first-order evolution equations on a Banach space X with dynamic boundary conditions, that is with boundary conditions containing time derivatives. Our method is based on the existence of an abstract Dirichlet operator and yields finally to equivalent systems of two simpler independent equations. In particular, we are led to an abstract Cauchy problem governed by an abstract Dirichlet-to-Neumann operator on the boundary space ∂ X . Our approach is illustrated by several examples and various generalizations are indicated. This article is part of the theme issue ‘Semigroup applications everywhere’.

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13

Kunze, Markus C. "Diffusion with nonlocal Dirichlet boundary conditions on domains." Studia Mathematica 253, no. 1 (2020): 1–38. http://dx.doi.org/10.4064/sm181012-24-5.

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14

Amster, P., and M. C. Mariani. "The prescribed mean curvature equation with Dirichlet conditions." Nonlinear Analysis: Theory, Methods & Applications 44, no. 1 (March 2001): 59–64. http://dx.doi.org/10.1016/s0362-546x(99)00247-3.

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15

Jankowski, Tadeusz. "Second order differential equations with Dirichlet boundary conditions." Integral Transforms and Special Functions 16, no. 3 (April 2005): 235–39. http://dx.doi.org/10.1080/1065246042000272045.

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16

Acevedo, Paul, Chérif Amrouche, and Carlos Conca. "Lptheory for Boussinesq system with Dirichlet boundary conditions." Applicable Analysis 98, no. 1-2 (October 19, 2018): 272–94. http://dx.doi.org/10.1080/00036811.2018.1530762.

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17

Slodička, M. "Semilinear parabolic problems with nonlocal Dirichlet boundary conditions." Inverse Problems in Science and Engineering 19, no. 5 (July 2011): 705–16. http://dx.doi.org/10.1080/17415977.2011.579608.

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18

Chen, Yunmei, and Fang Hua Lin. "Evolution of harmonic maps with Dirichlet boundary conditions." Communications in Analysis and Geometry 1, no. 3 (1993): 327–46. http://dx.doi.org/10.4310/cag.1993.v1.n3.a1.

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19

van den Berg, M., and P. B. Gilkey. "The heat equation with inhomogeneous Dirichlet boundary conditions." Communications in Analysis and Geometry 7, no. 2 (1999): 279–94. http://dx.doi.org/10.4310/cag.1999.v7.n2.a3.

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20

Haarsa, P., and S. Pothat. "On the homogeneous Dirichlet conditions for wave equation." Advanced Studies in Theoretical Physics 8 (2014): 655–60. http://dx.doi.org/10.12988/astp.2014.4552.

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21

Freitas, P., and D. Krejčiřík. "Waveguides with Combined Dirichlet and Robin Boundary Conditions." Mathematical Physics, Analysis and Geometry 9, no. 4 (February 16, 2007): 335–52. http://dx.doi.org/10.1007/s11040-007-9015-6.

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22

Eisenriegler, E. "Finite size critical behavior for Dirichlet boundary conditions." Zeitschrift f�r Physik B Condensed Matter 61, no. 3 (September 1985): 299–309. http://dx.doi.org/10.1007/bf01317797.

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23

Juarez-Campos, Beatriz. "Stochastic Schrödinger equation with Dirichlet noise boundary conditions." Journal of Mathematical Physics 62, no. 4 (April 1, 2021): 041506. http://dx.doi.org/10.1063/5.0030678.

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24

YAMNAHAKKI, A. "SECOND ORDER BOUNDARY CONDITIONS FOR THE DRIFT-DIFFUSION EQUATIONS OF SEMICONDUCTORS." Mathematical Models and Methods in Applied Sciences 05, no. 04 (June 1995): 429–55. http://dx.doi.org/10.1142/s0218202595000267.

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By an asymptotic analysis of the Boltzmann equation of semiconductors, we prove that Robin boundary conditions for drift-diffusion equations provide a more accurate fluid model than Dirichlet conditions. The Robin conditions involve the concept of the extrapolation length which we compute numerically. We compare the two-fluid models for a test problem. The numerical results show that the current density is correctly computed with Robin conditions. This is not the case with Dirichlet conditions.

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25

Jiang, Jun, Jinfeng Wang, and Yingwei Song. "The Influence of Dirichlet Boundary Conditions on the Dynamics for a Diffusive Predator–Prey System." International Journal of Bifurcation and Chaos 29, no. 09 (August 2019): 1950113. http://dx.doi.org/10.1142/s021812741950113x.

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A reaction–diffusion predator–prey system with homogeneous Dirichlet boundary conditions describes the lethal risk of predator and prey species on the boundary. The spatial pattern formations with the homogeneous Dirichlet boundary conditions are characterized by the Turing type linear instability of homogeneous state and bifurcation theory. Compared with homogeneous Neumann boundary conditions, we see that the homogeneous Dirichlet boundary conditions may depress the spatial patterns produced through the diffusion-induced instability. In addition, the existence of semi-trivial steady states and the global stability of the trivial steady state are characterized by the comparison technique.

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26

Bereanu, Cristian, and Jean Mawhin. "Existence and multiplicity results for nonlinear second order difference equations with Dirichlet boundary conditions." Mathematica Bohemica 131, no. 2 (2006): 145–60. http://dx.doi.org/10.21136/mb.2006.134087.

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27

Dehghani Tazehkand, I., and A. Jodayree Akbarfam. "An Inverse Spectral Problem for the Sturm-Liouville Operator on a Three-Star Graph." ISRN Applied Mathematics 2012 (May 27, 2012): 1–23. http://dx.doi.org/10.5402/2012/132842.

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We study an inverse spectral problem for the Sturm-Liouville operator on a three-star graph with the Dirichlet and Robin boundary conditions in the boundary vertices and matching conditions in the internal vertex. As spectral characteristics,we consider the spectrum of the main problem together with the spectra of two Dirichlet-Dirichlet problems and one Robin-Dirichlet problem on the edges of the graph and investigate their properties and asymptotic behavior. We prove that if these four spectra do not intersect, then the inverse problem of recovering the operator is uniquely solvable.We give an algorithm for the solution of the inverse problem with respect to this quadruple of spectra.

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28

Liang, Fei-Tsen. "Global boundedness, interior gradient estimates, and boundary regularity for the mean curvature equation with boundary conditions." International Journal of Mathematics and Mathematical Sciences 2004, no. 18 (2004): 913–48. http://dx.doi.org/10.1155/s0161171204307039.

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We obtain global estimates for the modulus, interior gradient estimates, and boundary Hölder continuity estimates for solutionsuto the capillarity problem and to the Dirichlet problem for the mean curvature equation merely in terms of the mean curvature, together with the boundary contact angle in the capillarity problem and the boundary values in the Dirichlet problem.

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29

BABUŠKA, IVO, VICTOR NISTOR, and NICOLAE TARFULEA. "APPROXIMATE AND LOW REGULARITY DIRICHLET BOUNDARY CONDITIONS IN THE GENERALIZED FINITE ELEMENT METHOD." Mathematical Models and Methods in Applied Sciences 17, no. 12 (December 2007): 2115–42. http://dx.doi.org/10.1142/s0218202507002571.

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We propose a method for treating Dirichlet boundary conditions for the Laplacian in the framework of the Generalized Finite Element Method (GFEM). A particular interest is taken in boundary data with low regularity (possibly a distribution). Our method is based on using approximate Dirichlet boundary conditions and polynomial approximations of the boundary. The sequence of GFEM-spaces consists of nonzero boundary value functions, and hence it does not conform to one of the basic Finite Element Method (FEM) conditions. We obtain quasi-optimal rates of convergence for the sequence of GFEM approximations of the exact solution. We also extend our results to the inhomogeneous Dirichlet boundary value problem, including the case when the boundary data has low regularity (i.e. is a distribution). Finally, we indicate an effective technique for constructing sequences of GFEM-spaces satisfying our assumptions by using polynomial approximations of the boundary.

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30

Kalita, Piotr, and Piotr Zgliczyński. "On non-autonomously forced Burgers equation with periodic and Dirichlet boundary conditions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 4 (March 14, 2019): 2025–54. http://dx.doi.org/10.1017/prm.2019.11.

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AbstractWe study the non-autonomously forced Burgers equation $$u_t(x,t) + u(x,t)u_x(x,t)-u_{xx}(x,t) = f(x,t)$$ on the space interval (0, 1) with two sets of the boundary conditions: the Dirichlet and periodic ones. For both situations we prove that there exists the unique H1 bounded trajectory of this equation defined for all t ∈ ℝ. Moreover we demonstrate that this trajectory attracts all trajectories both in pullback and forward sense. We also prove that for the Dirichlet case this attraction is exponential.

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31

Kolkovska, Ekaterina T. "On a stochastic Burgers equation with Dirichlet boundary conditions." International Journal of Mathematics and Mathematical Sciences 2003, no. 43 (2003): 2735–46. http://dx.doi.org/10.1155/s0161171203211121.

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We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.

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32

Buttazzo, Giuseppe, and Eugene Stepanov. "Transport density in Monge-Kantorovich problems with Dirichlet conditions." Discrete & Continuous Dynamical Systems - A 12, no. 4 (2005): 607–28. http://dx.doi.org/10.3934/dcds.2005.12.607.

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33

Altick, P. L. "Use of Dirichlet boundary conditions for electron-atom scattering." Physical Review A 38, no. 1 (July 1, 1988): 33–37. http://dx.doi.org/10.1103/physreva.38.33.

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34

Kamin, Shoshana, and Fabio Punzo. "Dirichlet conditions at infinity for parabolic and elliptic equations." Nonlinear Analysis 138 (June 2016): 156–75. http://dx.doi.org/10.1016/j.na.2015.11.001.

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35

Colorado, E., and I. Peral. "Semilinear elliptic problems with mixed Dirichlet–Neumann boundary conditions." Journal of Functional Analysis 199, no. 2 (April 2003): 468–507. http://dx.doi.org/10.1016/s0022-1236(02)00101-5.

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36

Izsák, Ferenc, and Gábor Maros. "Fractional order elliptic problems with inhomogeneous Dirichlet boundary conditions." Fractional Calculus and Applied Analysis 23, no. 2 (April 28, 2020): 378–89. http://dx.doi.org/10.1515/fca-2020-0018.

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AbstractFractional-order elliptic problems are investigated in case of inhomogeneous Dirichlet boundary data. The boundary integral form is proposed as a suitable mathematical model. The corresponding theory is completed by sharpening the mapping properties of the corresponding potential operators. The existence-uniqueness result is stated also for two-dimensional domains. Finally, a mild condition is provided to ensure the existence of the classical solution of the boundary integral equation.

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37

Bennour, H., and M. S. Said. "Numerical Solution of Poisson Equation with Dirichlet Boundary Conditions." International Journal of Open Problems in Computer Science and Mathematics 5, no. 4 (December 2012): 171–95. http://dx.doi.org/10.12816/0006149.

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38

Ashyralyev, Allaberen, and Fatma Songul Ozesenli Tetikoglu. "FDM for Elliptic Equations with Bitsadze-Samarskii-Dirichlet Conditions." Abstract and Applied Analysis 2012 (2012): 1–22. http://dx.doi.org/10.1155/2012/454831.

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A numerical method is proposed for solving nonlocal boundary value problem for the multidimensional elliptic partial differential equation with the Bitsadze-Samarskii-Dirichlet condition. The first and second-orders of accuracy stable difference schemes for the approximate solution of this nonlocal boundary value problem are presented. The stability estimates, coercivity, and almost coercivity inequalities for solution of these schemes are established. The theoretical statements for the solutions of these nonlocal elliptic problems are supported by results of numerical examples.

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39

Aksoylu, Burak, and Fatih Celiker. "Nonlocal problems with local Dirichlet and Neumann boundary conditions." Journal of Mechanics of Materials and Structures 12, no. 4 (May 20, 2017): 425–37. http://dx.doi.org/10.2140/jomms.2017.12.425.

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40

Hautefeuille, Martin, Chandrasekhar Annavarapu, and John E. Dolbow. "Robust imposition of Dirichlet boundary conditions on embedded surfaces." International Journal for Numerical Methods in Engineering 90, no. 1 (November 5, 2011): 40–64. http://dx.doi.org/10.1002/nme.3306.

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41

Sehlhorst, Hans-Georg, Alexander Düster, Ralf Jänicke, and Stefan Diebels. "On Dirichlet boundary conditions in second-order FE2-schemes." PAMM 10, no. 1 (November 16, 2010): 423–24. http://dx.doi.org/10.1002/pamm.201010204.

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42

Arada, N., and J. P. Raymond. "Optimality Conditions for State-Constrained Dirichlet Boundary Control Problems." Journal of Optimization Theory and Applications 102, no. 1 (July 1999): 51–68. http://dx.doi.org/10.1023/a:1021886227276.

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43

Alves, D. T., C. Farina, and P. A. Maia Neto. "Dynamical Casimir effect with Dirichlet and Neumann boundary conditions." Journal of Physics A: Mathematical and General 36, no. 44 (October 22, 2003): 11333–42. http://dx.doi.org/10.1088/0305-4470/36/44/011.

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44

Lunardi, A., G. Metafune, and D. Pallara. "Dirichlet boundary conditions for elliptic operators with unbounded drift." Proceedings of the American Mathematical Society 133, no. 9 (April 19, 2005): 2625–35. http://dx.doi.org/10.1090/s0002-9939-05-08068-8.

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45

Nualart, David, and Etienne Pardoux. "Second order stochastic differential equations with Dirichlet boundary conditions." Stochastic Processes and their Applications 39, no. 1 (October 1991): 1–24. http://dx.doi.org/10.1016/0304-4149(91)90028-b.

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46

Bazilevs, Y., and T. J. R. Hughes. "Weak imposition of Dirichlet boundary conditions in fluid mechanics." Computers & Fluids 36, no. 1 (January 2007): 12–26. http://dx.doi.org/10.1016/j.compfluid.2005.07.012.

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47

Englisch, H., and P. Šeba. "The stability of the Dirichlet and Neumann boundary conditions." Reports on Mathematical Physics 23, no. 3 (June 1986): 341–48. http://dx.doi.org/10.1016/0034-4877(86)90028-5.

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48

Kobayasi, Kazuo, and Dai Noboriguchi. "A Stochastic Conservation Law with Nonhomogeneous Dirichlet Boundary Conditions." Acta Mathematica Vietnamica 41, no. 4 (November 13, 2015): 607–32. http://dx.doi.org/10.1007/s40306-015-0157-5.

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49

Jebelean, Petru, and Constantin Popa. "Numerical solutions to singular ϕ-Laplacianwith Dirichlet boundary conditions." Numerical Algorithms 67, no. 2 (November 10, 2013): 305–18. http://dx.doi.org/10.1007/s11075-013-9792-x.

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50

Guo, Yujie, and Martin Ruess. "Weak Dirichlet boundary conditions for trimmed thin isogeometric shells." Computers & Mathematics with Applications 70, no. 7 (October 2015): 1425–40. http://dx.doi.org/10.1016/j.camwa.2015.06.012.

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