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Journal articles on the topic 'FREE-FREE BOUNDARY'

Author: Grafiati

Published: 11 September 2023

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1

Chistyakov, A. E., E. A. Protsenko, and E. F. Timofeeva. "Mathematical modeling of oscillatory processes with a free boundary." COMPUTATIONAL MATHEMATICS AND INFORMATION TECHNOLOGIES 1, no. 1 (2017): 102–12. http://dx.doi.org/10.23947/2587-8999-2017-1-1-102-112.

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2

Gurevich, Alex. "Boundary regularity for free boundary problems." Communications on Pure and Applied Mathematics 52, no. 3 (1999): 363–403. http://dx.doi.org/10.1002/(sici)1097-0312(199903)52:3<363::aid-cpa3>3.0.co;2-u.

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3

Jiang, Yingchun, and Qingqing Sun. "Three-Dimensional Biorthogonal Divergence-Free and Curl-Free Wavelets with Free-Slip Boundary." Journal of Applied Mathematics 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/954717.

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This paper deals with the construction of divergence-free and curl-free wavelets on the unit cube, which satisfies the free-slip boundary conditions. First, interval wavelets adapted to our construction are introduced. Then, we provide the biorthogonal divergence-free and curl-free wavelets with free-slip boundary and simple structure, based on the characterization of corresponding spaces. Moreover, the bases are also stable.

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4

SUSSMAN, MARK, and PETER SMEREKA. "Axisymmetric free boundary problems." Journal of Fluid Mechanics 341 (June 25, 1997): 269–94. http://dx.doi.org/10.1017/s0022112097005570.

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We present a number of three-dimensional axisymmetric free boundary problems for two immiscible fluids, such as air and water. A level set method is used where the interface is the zero level set of a continuous function while the two fluids are solutions of the incompressible Navier–Stokes equation. We examine the rise and distortion of an initially spherical bubble into cap bubbles and toroidal bubbles. Steady solutions for gas bubbles rising in a liquid are computed, with favourable comparisons to experimental data. We also study the inviscid limit and compare our results with a boundary in

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5

Dovì, V. G., H. Preisig, and O. Paladino. "Inverse free boundary problems." Applied Mathematics Letters 2, no. 1 (1989): 91–96. http://dx.doi.org/10.1016/0893-9659(89)90125-0.

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6

Lortz, D. "Plane free-boundary equilibria." Plasma Physics and Controlled Fusion 33, no. 1 (1991): 77–89. http://dx.doi.org/10.1088/0741-3335/33/1/005.

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7

Shargorodsky, E., and J. F. Toland. "Bernoulli free-boundary problems." Memoirs of the American Mathematical Society 196, no. 914 (2008): 0. http://dx.doi.org/10.1090/memo/0914.

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8

Park, Sung-Ho, and Juncheol Pyo. "Free boundary minimal hypersurfaces with spherical boundary." Mathematische Nachrichten 290, no. 5-6 (2016): 885–89. http://dx.doi.org/10.1002/mana.201500399.

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9

Edelen, Nick. "The free-boundary Brakke flow." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 758 (2020): 95–137. http://dx.doi.org/10.1515/crelle-2017-0053.

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AbstractWe develop the notion of Brakke flow with free-boundary in a barrier surface. Unlike the classical free-boundary mean curvature flow, the free-boundary Brakke flow must “pop” upon tangential contact with the barrier. We prove a compactness theorem for free-boundary Brakke flows, define a Gaussian monotonicity formula valid at all points, and use this to adapt the local regularity theorem of White [23] to the free-boundary setting. Using Ilmanen’s elliptic regularization procedure [10], we prove existence of free-boundary Brakke flows.

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10

MATSUSHITA, Osami. "Modelling; Free from boundary condition." Journal of the Japan Society for Precision Engineering 54, no. 5 (1988): 848–52. http://dx.doi.org/10.2493/jjspe.54.848.

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11

Mendes, Abraão. "Rigidity of free boundary MOTS." Nonlinear Analysis 220 (July 2022): 112841. http://dx.doi.org/10.1016/j.na.2022.112841.

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12

Agelmenev, M. E. "The Modeling with Free Boundary." Molecular Crystals and Liquid Crystals 545, no. 1 (2011): 190/[1414]—203/[1427]. http://dx.doi.org/10.1080/15421406.2011.572010.

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13

Hilhorst, Danielle, and Josephus Hulshof. "A free boundary focusing problem." Proceedings of the American Mathematical Society 121, no. 4 (1994): 1193. http://dx.doi.org/10.1090/s0002-9939-1994-1233975-9.

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14

Dipierro, Serena, Ovidiu Savin, and Enrico Valdinoci. "A Nonlocal Free Boundary Problem." SIAM Journal on Mathematical Analysis 47, no. 6 (2015): 4559–605. http://dx.doi.org/10.1137/140999712.

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15

Friedman, Avner. "Free boundary problems in biology." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373, no. 2050 (2015): 20140368. http://dx.doi.org/10.1098/rsta.2014.0368.

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In this paper, I review several free boundary problems that arise in the mathematical modelling of biological processes. The biological topics are quite diverse: cancer, wound healing, biofilms, granulomas and atherosclerosis. For each of these topics, I describe the biological background and the mathematical model, and then proceed to state mathematical results, including existence and uniqueness theorems, stability and asymptotic limits, and the behaviour of the free boundary. I also suggest, for each of the topics, open mathematical problems.

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16

Zheng, L. J. "Free boundary ballooning mode representation." Physics of Plasmas 19, no. 10 (2012): 102506. http://dx.doi.org/10.1063/1.4759012.

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17

Nührenberg, C. "Free-boundary perturbed MHD equilibria." Journal of Physics: Conference Series 401 (December 3, 2012): 012018. http://dx.doi.org/10.1088/1742-6596/401/1/012018.

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18

Soltanov, K. N., and E. B. Novruzov. "On a free boundary problem." Izvestiya: Mathematics 66, no. 4 (2002): 807–27. http://dx.doi.org/10.1070/im2002v066n04abeh000398.

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19

Bensid, Sabri, and S. M. Bouguima. "On a free boundary problem." Nonlinear Analysis: Theory, Methods & Applications 68, no. 8 (2008): 2328–48. http://dx.doi.org/10.1016/j.na.2007.01.047.

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20

Frolova, E. V. "Free Boundary Problem of Magnetohydrodynamics." Journal of Mathematical Sciences 210, no. 6 (2015): 857–77. http://dx.doi.org/10.1007/s10958-015-2596-x.

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21

Chen, Eugene Y., H. L. Berk, B. Breizman, and L. J. Zheng. "Free-boundary toroidal Alfvén eigenmodes." Physics of Plasmas 18, no. 5 (2011): 052503. http://dx.doi.org/10.1063/1.3575157.

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22

Cryer, Colin C., and John Crank. "Free and Moving Boundary Problems." Mathematics of Computation 46, no. 174 (1986): 765. http://dx.doi.org/10.2307/2008018.

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23

CRASTER, R. V. "Two related free boundary problems." IMA Journal of Applied Mathematics 52, no. 3 (1994): 253–70. http://dx.doi.org/10.1093/imamat/52.3.253.

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24

Remizova, E. V. "A problem with free boundary." Journal of Soviet Mathematics 45, no. 3 (1989): 1163–72. http://dx.doi.org/10.1007/bf01096148.

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25

Boucherif, Abdelkader, and Sidi Mohammed Bouguima. "On a Free Boundary Problem." Mathematical Methods in the Applied Sciences 19, no. 15 (1996): 1257–64. http://dx.doi.org/10.1002/(sici)1099-1476(199610)19:15<1257::aid-mma834>3.0.co;2-t.

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26

Clarelli, Fabrizio, Antonio Fasano, and Roberto Natalini. "Free-boundary models of sulphation." PAMM 7, no. 1 (2007): 1110201–2. http://dx.doi.org/10.1002/pamm.200700288.

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27

Kuznetsov, V. V., and O. A. Frolovskaya. "Boundary layers in free convection." Journal of Applied Mechanics and Technical Physics 41, no. 3 (2000): 461–69. http://dx.doi.org/10.1007/bf02465297.

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28

Mikayelyan, Hayk, and Henrik Shahgholian. "Convexity of the free boundary for an exterior free boundary problem involving the perimeter." Communications on Pure & Applied Analysis 12, no. 3 (2013): 1431–43. http://dx.doi.org/10.3934/cpaa.2013.12.1431.

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29

Centen, P., M. P. H. Weenink, and W. Schuurman. "Minimum-energy principle for a free-boundary, force-free plasma." Plasma Physics and Controlled Fusion 28, no. 1B (1986): 347–55. http://dx.doi.org/10.1088/0741-3335/28/1b/009.

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30

Gupta, A. K., and D. Surya. "Benard-Marangoni Convection with Free Slip Bottom and Mixed Thermal Boundary Conditions." Mathematical Journal of Interdisciplinary Sciences 2, no. 2 (2014): 141–54. http://dx.doi.org/10.15415/mjis.2014.22011.

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31

Okuma, Masaaki, and Qinzhong Shi. "Identification of Principal Rigid Body Modes Under Free-Free Boundary Condition." Journal of Vibration and Acoustics 119, no. 3 (1997): 341–45. http://dx.doi.org/10.1115/1.2889729.

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This paper focuses on the problem of identifying all individual principal rigid body modes and the associated mass or principal inertia of moment, which can be called modal mass, of flexible structures under the free-free boundary condition with fewer multi-location excitations than the number of those modes. The rigid body mass matrix of the structure can be identified by using both the parameters of inertia, which are determined previously by a modal parameter estimation, and the coordinates of measurement points. As all rigid body properties can be obtained from the mass matrix, it becomes

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32

Yi,, Tong Y., and Parviz E. Nikravesh. "Extraction of Free-Free Modes from Constrained Vibration Data for Flexible Multibody Models." Journal of Vibration and Acoustics 123, no. 3 (2001): 383–89. http://dx.doi.org/10.1115/1.1375814.

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This paper presents a method for identifying the free-free modes of a structure by utilizing the vibration data of the same structure with boundary conditions. In modal formulations for flexible body dynamics, modal data are primary known quantities that are obtained either experimentally or analytically. The vibration measurements may be obtained for a flexible body that is constrained differently than its boundary conditions in a multibody system. For a flexible body model in a multibody system, depending upon the formulation used, we may need a set of free-free modal data or a set of constr

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33

Samira, Khatmi, and Barkatou Mohammed. "On some overdetermined free boundary problems." ANZIAM Journal 49 (November 22, 2007): 11. http://dx.doi.org/10.21914/anziamj.v49i0.168.

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34

Hussein, M. S., D. Lesnic, and M. Ivanchov. "Free Boundary Determination in Nonlinear Diffusion." East Asian Journal on Applied Mathematics 3, no. 4 (2013): 295–310. http://dx.doi.org/10.4208/eajam.100913.061113a.

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AbstractFree boundary problems with nonlinear diffusion occur in various applications, such as solidification over a mould with dissimilar nonlinear thermal properties and saturated or unsaturated absorption in the soil beneath a pond. In this article, we consider a novel inverse problem where a free boundary is determined from the mass/energy specification in a well-posed one-dimensional nonlinear diffusion problem, and a stability estimate is established. The problem is recast as a nonlinear least-squares minimisation problem, which is solved numerically using the lsqnonlin routine from the

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35

Friedman, Avner. "Free boundary problems arising in biology." Discrete & Continuous Dynamical Systems - B 23, no. 1 (2018): 193–202. http://dx.doi.org/10.3934/dcdsb.2018013.

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36

S., L. R., and P. Neittaanmaki. "Numerical Methods for Free Boundary Problems." Mathematics of Computation 63, no. 207 (1994): 426. http://dx.doi.org/10.2307/2153589.

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37

KIM, INWON C. "A Free Boundary Problem with Curvature." Communications in Partial Differential Equations 30, no. 1-2 (2005): 121–38. http://dx.doi.org/10.1081/pde-200044474.

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38

Huysmans, G. T. A., J. P. Goedbloed, and W. Kerner. "Free boundary resistive modes in tokamaks." Physics of Fluids B: Plasma Physics 5, no. 5 (1993): 1545–58. http://dx.doi.org/10.1063/1.860894.

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39

Lewis, John L., and Andrew L. Vogel. "Uniqueness in a Free Boundary Problem." Communications in Partial Differential Equations 31, no. 11 (2006): 1591–614. http://dx.doi.org/10.1080/03605300500455909.

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40

Lamboley, Jimmy, Yannick Sire, and Eduardo V. Teixeira. "Free boundary problems involving singular weights." Communications in Partial Differential Equations 45, no. 7 (2020): 758–75. http://dx.doi.org/10.1080/03605302.2020.1716003.

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41

Reusch, Michael F. "Free boundary skin current magnetohydrodynamic equilibria." Physics of Fluids 31, no. 10 (1988): 2962. http://dx.doi.org/10.1063/1.866953.

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42

De Silva, Daniela, and David Jerison. "A singular energy minimizing free boundary." Journal für die reine und angewandte Mathematik (Crelles Journal) 2009, no. 635 (2009): 1–21. http://dx.doi.org/10.1515/crelle.2009.074.

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43

Hongler, Clément, and Kalle Kytölä. "Ising interfaces and free boundary conditions." Journal of the American Mathematical Society 26, no. 4 (2013): 1107–89. http://dx.doi.org/10.1090/s0894-0347-2013-00774-2.

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44

Emamizadeh, B., and M. Marras. "Rearrangement Optimization Problems with Free Boundary." Numerical Functional Analysis and Optimization 35, no. 4 (2014): 404–22. http://dx.doi.org/10.1080/01630563.2014.884587.

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45

CHIPPADA, S., T. C. JUE, S. W. JOO, M. F. WHEELER, and B. RAMASWAMY. "Numerical Simulation of Free-Boundary Problems." International Journal of Computational Fluid Dynamics 7, no. 1-2 (1996): 91–118. http://dx.doi.org/10.1080/10618569608940754.

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46

Clain, S. "Chemical Attack in Free Boundary Domains." Journal of Applied Analysis 5, no. 1 (1999): 35–58. http://dx.doi.org/10.1515/jaa.1999.35.

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47

Hou, Thomas Y. "Numerical Solutions to Free Boundary Problems." Acta Numerica 4 (January 1995): 335–415. http://dx.doi.org/10.1017/s0962492900002567.

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Many physically interesting problems involve propagation of free surfaces. Vortex-sheet roll-up in hydrodynamic instability, wave interactions on the ocean's free surface, the solidification problem for crystal growth and Hele-Shaw cells for pattern formation are some of the significant examples. These problems present a great challenge to physicists and applied mathematicians because the underlying problem is very singular. The physical solution is sensitive to small perturbations. Naïve discretisations may lead to numerical instabilities. Other numerical difficulties include singularity form

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48

Fotouhi, Morteza, and Henrik Shahgholian. "A semilinear PDE with free boundary." Nonlinear Analysis: Theory, Methods & Applications 151 (March 2017): 145–63. http://dx.doi.org/10.1016/j.na.2016.11.019.

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49

BERON-VERA, F. J., and P. RIPA. "Free boundary effects on baroclinic instability." Journal of Fluid Mechanics 352 (December 10, 1997): 245–64. http://dx.doi.org/10.1017/s0022112097007222.

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The effects of a free boundary on the stability of a baroclinic parallel flow are investigated using a reduced-gravity model. The basic state has uniform density stratification and a parallel flow with uniform vertical shear in thermal-wind balance with the horizontal buoyancy gradient. A finite value of the velocity at the free (lower) boundary requires the interface to have a uniform slope in the direction transversal to that of the flow. Normal-mode perturbations with arbitrary vertical structure are studied in the limit of small Rossby number. This solution is restricted to neither a horiz

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50

Lions, P. L., and N. Masmoudi. "On a free boundary barotropic model." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 16, no. 3 (1999): 373–410. http://dx.doi.org/10.1016/s0294-1449(99)80018-3.

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