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Journal articles on the topic 'Heat flow harmonic maps'

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Published: 10 December 2022
Last updated: 29 January 2023

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1

Wang, Changyou, and Tao Huang. "On uniqueness of heat flow of harmonic maps." Indiana University Mathematics Journal 65, no. 5 (2016): 1525–46. http://dx.doi.org/10.1512/iumj.2016.65.5894.

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2

Coron, J. M. "Nonuniqueness for the heat flow of harmonic maps." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 7, no. 4 (July 1990): 335–44. http://dx.doi.org/10.1016/s0294-1449(16)30295-5.

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3

Wang, Meng, and Xiao-feng Liu. "Heat flow of harmonic maps from noncompact manifolds." Applied Mathematics-A Journal of Chinese Universities 23, no. 4 (December 2008): 431–36. http://dx.doi.org/10.1007/s11766-008-1604-z.

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4

Xin, Yuanlong. "Heat flow of equivariant harmonic maps from 𝔹3into ℂℙ2." Pacific Journal of Mathematics 176, no. 2 (December 1, 1996): 563–79. http://dx.doi.org/10.2140/pjm.1996.176.563.

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5

LI, JIAYU, and SILEI WANG. "THE HEAT FLOW OF HARMONIC MAPS FROM NONCOMPACT MANIFOLDS." Chinese Annals of Mathematics 21, no. 01 (January 2000): 121–30. http://dx.doi.org/10.1142/s0252959900000169.

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6

Huang, Pingliang, and Hongyan Tang. "On the heat flow of -harmonic maps from into." Nonlinear Analysis: Theory, Methods & Applications 67, no. 7 (October 2007): 2149–56. http://dx.doi.org/10.1016/j.na.2006.09.020.

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7

Wang, Meng. "The heat flow of harmonic maps from noncompact manifolds." Nonlinear Analysis: Theory, Methods & Applications 71, no. 3-4 (August 2009): 1042–48. http://dx.doi.org/10.1016/j.na.2008.11.029.

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8

Kung-Ching, Chang. "Heat flow and boundary value problem for harmonic maps." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 6, no. 5 (September 1989): 363–95. http://dx.doi.org/10.1016/s0294-1449(16)30316-x.

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9

Wang, Jiaping. "The heat flow and harmonic maps between complete manifolds." Journal of Geometric Analysis 8, no. 3 (September 1998): 485–514. http://dx.doi.org/10.1007/bf02921799.

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10

Chen, Yunmei, Min-Chun Hong, and Norbert Hungerbühler. "Heat flow ofp-harmonic maps with values into spheres." Mathematische Zeitschrift 215, no. 1 (January 1994): 25–35. http://dx.doi.org/10.1007/bf02571698.

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11

Li, Zhen Yang, and Xi Zhang. "Hermitian Harmonic Maps into Convex Balls." Canadian Mathematical Bulletin 50, no. 1 (March 1, 2007): 113–22. http://dx.doi.org/10.4153/cmb-2007-011-1.

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AbstractIn this paper, we consider Hermitian harmonic maps from Hermitian manifolds into convex balls. We prove that there exist no non-trivial Hermitian harmonic maps from closed Hermitian manifolds into convex balls, and we use the heat flow method to solve the Dirichlet problem for Hermitian harmonic maps when the domain is a compact Hermitian manifold with non-empty boundary.
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12

Baird, Paul, Ali Fardoun, and Rachid Regbaoui. "Heat flow for harmonic maps from graphs into Riemannian manifolds." Journal of Geometry and Physics 176 (June 2022): 104496. http://dx.doi.org/10.1016/j.geomphys.2022.104496.

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13

Fardoun, Ali, and Rachid Regbaoui. "Heat flow for p-harmonic maps between compact Riemannian manifolds." Indiana University Mathematics Journal 51, no. 6 (2002): 1305–20. http://dx.doi.org/10.1512/iumj.2002.51.2176.

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14

Fardoun, Ali, and Rachid Regbaoui. "Heat flow for p -harmonic maps with small initial data." Calculus of Variations and Partial Differential Equations 16, no. 1 (January 1, 2003): 1–16. http://dx.doi.org/10.1007/s005260100138.

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15

Zhang, Xiao. "The heat flow and harmonic maps on a class of manifolds." Pacific Journal of Mathematics 182, no. 1 (January 1, 1998): 157–82. http://dx.doi.org/10.2140/pjm.1998.182.157.

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16

Bertsch, Michiel, Roberta Dal Passo, and Adriano Pisante. "Point Singularities and Nonuniqueness for the Heat Flow for Harmonic Maps." Communications in Partial Differential Equations 28, no. 5-6 (January 7, 2003): 1135–60. http://dx.doi.org/10.1081/pde-120021189.

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17

Courilleau, Patrick, and Françoise Demengel. "Heat flow for p-harmonic maps with values in the circle." Nonlinear Analysis: Theory, Methods & Applications 41, no. 5-6 (August 2000): 689–700. http://dx.doi.org/10.1016/s0362-546x(98)00304-6.

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18

Soyeur, A. "A Global Existence Result For The Heat Flow of Harmonic Maps." Communications in Partial Differential Equations 15, no. 2 (January 1990): 237–44. http://dx.doi.org/10.1080/03605309908820685.

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19

Not Available, Michiel Bertsch, Roberta Dal Passo, and Rein van der Hout. "Nonuniqueness for the Heat Flow¶of Harmonic Maps on the Disk." Archive for Rational Mechanics and Analysis 161, no. 2 (February 1, 2002): 93–112. http://dx.doi.org/10.1007/s002050100171.

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20

Gui, Xinping, Buyang Li, and Jilu Wang. "Convergence of Renormalized Finite Element Methods for Heat Flow of Harmonic Maps." SIAM Journal on Numerical Analysis 60, no. 1 (February 2022): 312–38. http://dx.doi.org/10.1137/21m1402212.

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21

Boegelein, Verena, Frank Duzaar, and Christoph Scheven. "Global solutions to the heat flow for $m$-harmonic maps and regularity." Indiana University Mathematics Journal 61, no. 6 (2012): 2157–210. http://dx.doi.org/10.1512/iumj.2012.61.4819.

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22

Chen, Chao-Nien, L. F. Cheung, Y. S. Choi, and C. K. Law. "On the blow-up of heat flow for conformal $3$-harmonic maps." Transactions of the American Mathematical Society 354, no. 12 (July 16, 2002): 5087–110. http://dx.doi.org/10.1090/s0002-9947-02-03054-4.

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23

Chen, Yunmei, and Michael Struwe. "Existence and partial regularity results for the heat flow for harmonic maps." Mathematische Zeitschrift 201, no. 1 (March 1989): 83–103. http://dx.doi.org/10.1007/bf01161997.

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24

Chen, Yunmei, and Livio Flaminio. "Removability of the singular set of the heat flow of harmonic maps." Proceedings of the American Mathematical Society 124, no. 2 (1996): 513–25. http://dx.doi.org/10.1090/s0002-9939-96-03169-3.

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25

Moser, Roger. "Regularity for the approximated harmonic map equation and application to the heat flow for harmonic maps." Mathematische Zeitschrift 243, no. 2 (February 1, 2003): 263–89. http://dx.doi.org/10.1007/s00209-002-0463-1.

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26

Fan, Huijun. "Existence of the self-similar solutions in the heat flow of harmonic maps." Science in China Series A: Mathematics 42, no. 2 (February 1999): 113–32. http://dx.doi.org/10.1007/bf02876563.

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27

Pu, Xueke, and Boling Guo. "The fractional Landau–Lifshitz–Gilbert equation and the heat flow of harmonic maps." Calculus of Variations and Partial Differential Equations 42, no. 1-2 (October 12, 2010): 1–19. http://dx.doi.org/10.1007/s00526-010-0377-4.

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28

Chang, Kung-Ching, Wei Yue Ding, and Rugang Ye. "Finite-time blow-up of the heat flow of harmonic maps from surfaces." Journal of Differential Geometry 36, no. 2 (1992): 507–15. http://dx.doi.org/10.4310/jdg/1214448751.

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29

Qing, Jie. "On singularities of the heat flow for harmonic maps from surfaces into spheres." Communications in Analysis and Geometry 3, no. 2 (1995): 297–315. http://dx.doi.org/10.4310/cag.1995.v3.n2.a4.

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30

Jost, Jürgen, and Yi-Hu Yang. "Heat flow for horizontal harmonic maps into a class of Carnot-Caratheodory spaces." Mathematical Research Letters 12, no. 4 (2005): 513–29. http://dx.doi.org/10.4310/mrl.2005.v12.n4.a6.

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31

Qiu, Hongbing. "The heat flow of $V$-harmonic maps from complete manifolds into regular balls." Proceedings of the American Mathematical Society 145, no. 5 (January 27, 2017): 2271–80. http://dx.doi.org/10.1090/proc/13332.

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32

Lin, Fanghua, and Changyou Wang. "On the uniqueness of heat flow of harmonic maps and hydrodynamic flow of nematic liquid crystals." Chinese Annals of Mathematics, Series B 31, no. 6 (October 22, 2010): 921–38. http://dx.doi.org/10.1007/s11401-010-0612-5.

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33

Hamza, Valiya Mannathal, and Fábio Vieira. "Global Heat Flow: New Estimates Using Digital Maps and GIS Techniques." International Journal of Terrestrial Heat Flow and Applications 1, no. 1 (April 26, 2018): 6–13. http://dx.doi.org/10.31214/ijthfa.v1i1.6.

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The digital geophysical maps and GIS (Geographic Information System) techniques have been employed in obtaining a better understanding of global heat flow. The starting point has been a system of 1o x 1o equal longitude grid consisting of 64800 cells. Superposed on this grid system are a set of 190 polygons that approximates boundaries of tectonic provinces and another set of 137 polygons that outlines age provinces. The area extents of these “tectonic polygons” were determined, and heat flow values calculated based on the empirical relation between heat flow and age of last thermos-tectonic event. Maps derived using such polygon representations reveal a pattern quite similar to that obtained in higher-degree spherical harmonic representations of global heat flow. In addition, an updated assessment of observational data has been carried out and estimated values assigned for cells where observational data are currently unavailable. This practice has been found to provide reasonable bounds in interpolations, leading to better representations of heat flow on a global scale. The mean global heat flow values obtained by this procedure is found to fall in the interval of 58 to 63mW/m². This estimate is lower than that reported in some of the previous studies in which use has been made of theoretical values derived from half-space cooling models as substitutes for experimental data. According to the results of the present work, based on reappraisal of global heat flow database and with due emphasis on observational data, the global conductive heat loss falls in the range of 28 to 35TW. This is nearly 22 to 35% less than those reported in earlier studies.
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34

Misawa, Masashi. "Local regularity and compactness for the p-harmonic map heat flows." Advances in Calculus of Variations 11, no. 3 (July 1, 2018): 223–55. http://dx.doi.org/10.1515/acv-2016-0064.

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AbstractWe study a geometric analysis and local regularity for the evolution of {{p}}-harmonic maps, called {{p}}-harmonic map heat flows. Our main result is to establish a criterion for a uniform local regularity estimate for regular {{p}}-harmonic map heat flows, devising some new monotonicity-type formulas of a local scaled energy. The regularity criterion obtained is almost optimal, comparing with that of the corresponding stationary case. As application we show a compactness of regular {{p}}-harmonic map heat flows with energy bound.
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35

Thalmaier, Anton. "Brownian motion and the formation of singularities in the heat flow for harmonic maps." Probability Theory and Related Fields 105, no. 3 (July 1, 1996): 335–67. http://dx.doi.org/10.1007/s004400050047.

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36

Qing, Jie. "A remark on the finite time singularity of the heat flow for harmonic maps." Calculus of Variations and Partial Differential Equations 17, no. 4 (August 1, 2003): 393–403. http://dx.doi.org/10.1007/s00526-002-0176-7.

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37

Thalmaier, Anton. "Brownian motion and the formation of singularities in the heat flow for harmonic maps." Probability Theory and Related Fields 105, no. 3 (September 1996): 335–67. http://dx.doi.org/10.1007/bf01192212.

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38

Biernat, Paweł. "Non-self-similar blow-up in the heat flow for harmonic maps in higher dimensions." Nonlinearity 28, no. 1 (December 11, 2014): 167–85. http://dx.doi.org/10.1088/0951-7715/28/1/167.

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39

Wang, Changyou. "Heat Flow of Harmonic Maps Whose Gradients Belong to $$L^{n}_{x}L^{\infty}_{t}$$." Archive for Rational Mechanics and Analysis 188, no. 2 (February 2, 2008): 351–69. http://dx.doi.org/10.1007/s00205-007-0102-4.

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40

Wang, Changyou. "Well-posedness for the heat flow of harmonic maps and the liquid crystal flow with rough initial data." Archive for Rational Mechanics and Analysis 200, no. 1 (July 27, 2010): 1–19. http://dx.doi.org/10.1007/s00205-010-0343-5.

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41

Carfora, Mauro. "The Wasserstein geometry of nonlinear σ models and the Hamilton–Perelman Ricci flow." Reviews in Mathematical Physics 29, no. 01 (January 10, 2017): 1750001. http://dx.doi.org/10.1142/s0129055x17500015.

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Nonlinear sigma models are quantum field theories describing, in the large deviation sense, random fluctuations of harmonic maps between a Riemann surface and a Riemannian manifold. Via their formal renormalization group analysis, they provide a framework for possible generalizations of the Hamilton–Perelman Ricci flow. By exploiting the heat kernel embedding introduced by Gigli and Mantegazza, we show that the Wasserstein geometry of the space of probability measures over Riemannian metric measure spaces provides a natural setting for discussing the relation between nonlinear sigma models and Ricci flow theory. In particular, we analyze the embedding of Ricci flow into a heat kernel renormalization group flow for dilatonic nonlinear sigma models, and characterize a non-trivial generalization of the Hamilton–Perelman version of the Ricci flow. We discuss in detail the monotonicity and gradient flow properties of this extended flow.
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42

Dai, Junfei, Wei Luo, and Meng Wang. "A note on the heat flow of harmonic maps whose gradients belong to $L^q_t L^p_x$." Pure and Applied Mathematics Quarterly 11, no. 2 (2015): 283–92. http://dx.doi.org/10.4310/pamq.2015.v11.n2.a5.

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43

Jost, Jürgen, Lei Liu, and Miaomiao Zhu. "A mixed elliptic-parabolic boundary value problem coupling a harmonic-like map with a nonlinear spinor." Journal für die reine und angewandte Mathematik (Crelles Journal) 2022, no. 785 (February 15, 2022): 81–116. http://dx.doi.org/10.1515/crelle-2021-0085.

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Abstract In this paper, we solve a new elliptic-parabolic system arising in geometric analysis that is motivated by the nonlinear supersymmetric sigma model of quantum field theory. The corresponding action functional involves two fields, a map from a Riemann surface into a Riemannian manifold and a spinor coupled to the map. The first field has to satisfy a second-order elliptic system, which we turn into a parabolic system so as to apply heat flow techniques. The spinor, however, satisfies a first-order Dirac-type equation. We carry that equation as a nonlinear constraint along the flow. With this novel scheme, in more technical terms, we can show the existence of Dirac-harmonic maps from a compact spin Riemann surface with smooth boundary to a general compact Riemannian manifold via a heat flow method when a Dirichlet boundary condition is imposed on the map and a chiral boundary condition on the spinor.
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44

Feehan, Paul M. N., and Manousos Maridakis. "Łojasiewicz–Simon gradient inequalities for analytic and Morse–Bott functions on Banach spaces." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 765 (August 1, 2020): 35–67. http://dx.doi.org/10.1515/crelle-2019-0029.

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AbstractWe prove several abstract versions of the Łojasiewicz–Simon gradient inequality for an analytic function on a Banach space that generalize previous abstract versions of this inequality, weakening their hypotheses and, in particular, that of the well-known infinite-dimensional version of the gradient inequality due to Łojasiewicz [S. Łojasiewicz, Ensembles semi-analytiques, (1965), Publ. Inst. Hautes Etudes Sci., Bures-sur-Yvette. LaTeX version by M. Coste, August 29, 2006 based on mimeographed course notes by S. Łojasiewicz, https://perso.univ-rennes1.fr/michel.coste/Lojasiewicz.pdf] and proved by Simon [L. Simon, Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems, Ann. of Math. (2) 118 1983, 3, 525–571]. We prove that the optimal exponent of the Łojasiewicz–Simon gradient inequality is obtained when the function is Morse–Bott, improving on similar results due to Chill [R. Chill, On the Łojasiewicz–Simon gradient inequality, J. Funct. Anal. 201 2003, 2, 572–601], [R. Chill, The Łojasiewicz–Simon gradient inequality in Hilbert spaces, Proceedings of the 5th European-Maghrebian workshop on semigroup theory, evolution equations, and applications 2006, 25–36], Haraux and Jendoubi [A. Haraux and M. A. Jendoubi, On the convergence of global and bounded solutions of some evolution equations, J. Evol. Equ. 7 2007, 3, 449–470], and Simon [L. Simon, Theorems on regularity and singularity of energy minimizing maps, Lect. Math. ETH Zürich, Birkhäuser, Basel 1996]. In [P. M. N. Feehan and M. Maridakis, Łojasiewicz–Simon gradient inequalities for harmonic maps, preprint 2019, https://arxiv.org/abs/1903.01953], we apply our abstract gradient inequalities to prove Łojasiewicz–Simon gradient inequalities for the harmonic map energy function using Sobolev spaces which impose minimal regularity requirements on maps between closed, Riemannian manifolds. Those inequalities generalize those of Kwon [H. Kwon, Asymptotic convergence of harmonic map heat flow, ProQuest LLC, Ann Arbor 2002; Ph.D. thesis, Stanford University, 2002], Liu and Yang [Q. Liu and Y. Yang, Rigidity of the harmonic map heat flow from the sphere to compact Kähler manifolds, Ark. Mat. 48 2010, 1, 121–130], Simon [L. Simon, Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems, Ann. of Math. (2) 118 1983, 3, 525–571], [L. Simon, Isolated singularities of extrema of geometric variational problems, Harmonic mappings and minimal immersions (Montecatini 1984), Lecture Notes in Math. 1161, Springer, Berlin 1985, 206–277], and Topping [P. M. Topping, Rigidity in the harmonic map heat flow, J. Differential Geom. 45 1997, 3, 593–610]. In [P. M. N. Feehan and M. Maridakis, Łojasiewicz–Simon gradient inequalities for coupled Yang–Mills energy functions, preprint 2019, https://arxiv.org/abs/1510.03815v6; to appear in Mem. Amer. Math. Soc.], we prove Łojasiewicz–Simon gradient inequalities for coupled Yang–Mills energy functions using Sobolev spaces which impose minimal regularity requirements on pairs of connections and sections. Those inequalities generalize that of the pure Yang–Mills energy function due to the first author [P. M. N. Feehan, Global existence and convergence of solutions to gradient systems and applications to Yang–Mills gradient flow, preprint 2016, https://arxiv.org/abs/1409.1525v4] for base manifolds of arbitrary dimension and due to Råde [J. Råde, On the Yang–Mills heat equation in two and three dimensions, J. reine angew. Math. 431 1992, 123–163] for dimensions two and three.
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45

Biernat, Paweł, and Piotr Bizoń. "Shrinkers, expanders, and the unique continuation beyond generic blowup in the heat flow for harmonic maps between spheres." Nonlinearity 24, no. 8 (June 16, 2011): 2211–28. http://dx.doi.org/10.1088/0951-7715/24/8/005.

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46

Lin, Junyu, and Shijin Ding. "On the well-posedness for the heat flow of harmonic maps and the hydrodynamic flow of nematic liquid crystals in critical spaces." Mathematical Methods in the Applied Sciences 35, no. 2 (December 30, 2011): 158–73. http://dx.doi.org/10.1002/mma.1548.

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47

Morales, Ethel, Agostina Pedro, and Ricardo De León. "Geothermal Gradients and Heat Flow in Norte Basin of Uruguay." International Journal of Terrestrial Heat Flow and Applications 3, no. 1 (March 10, 2020): 20–25. http://dx.doi.org/10.31214/ijthfa.v3i1.43.

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Progress obtained in a partial update of geothermal gradient and terrestrial heat flow values for the Norte Basin (Uruguay) are presented. It is based on results of temperature measurements carried out in deep water wells. Most of these wells have intersected the southern part of the Guarani Aquifer System, at depths varying from 200 to 1500m. In most of the Norte Basin it is a confined aquifer capped by the flood basalts of Cretaceous age. The results indicate that temperature gradients fall in the range of 15 to 45oC/km and the thermal conductivity of basalts have a mean value of 2.2W/m/K. Analysis of temperature distributions indicate that heat transfer takes place not only by conduction but also by upflow of groundwater with velocities in the range of 10-9 to 10-8 m/s. The representative mean heat flow values fall in the range of 30 to 85mW/m2. Maps of spatial distributions of geothermal gradients and heat flow values have been considered as indicative of the possible existence of an anomalous geothermal zone in the central-northwestern part of the Norte Basin. There are indications that this anomalous geothermal zone extends also to the eastern parts of adjacent regions in Argentina. Theoretical values derived on the basis of spherical harmonic expansion, employed in estimating geothermal gradients and heat flow points to a zone of relatively low heat flow in the other regions of the Norte Basin.
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48

Gustafson, Stephen, Kenji Nakanishi, and Tai-Peng Tsai. "Asymptotic Stability, Concentration, and Oscillation in Harmonic Map Heat-Flow, Landau-Lifshitz, and Schrödinger Maps on $${\mathbb R^2}$$." Communications in Mathematical Physics 300, no. 1 (August 21, 2010): 205–42. http://dx.doi.org/10.1007/s00220-010-1116-6.

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49

Soares, Willames Albuquerque. "Análise Comparativa do Fluxo de Calor no Solo em Profundidade e na Superfície (Brazil Comparative Analysis of Soil Heat Flux in Depth and Surface)." Revista Brasileira de Geografia Física 6, no. 4 (November 14, 2013): 665. http://dx.doi.org/10.26848/rbgf.v6i4.233057.

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O objetivo deste estudo é comparar os resultados do fluxo de calor no solo, na superfície e em profundidade, encontrados por sensores de fluxo de calor no solo e pelo método harmônico, em cultivo de mamoneira. No dia sem chuvas, a pouca quantidade de água no solo diminuiu a sua difusividade térmica, provocando um maior acúmulo de energia no solo, e, consequentemente, a elevação na temperatura nas camadas mais próximas à superfície. As principais diferenças entre os valores medidos e estimados aconteceram nos horários de maior insolação, principalmente nos dias em que o céu estava encoberto por nuvens. A presença da vegetação cobrindo o solo influenciou diretamente nos valores medidos e modelados. As estimativas tanto em profundidade como para a superfície do solo se mostraram bastante satisfatórias, tanto em dias de céu claro como para dias de céu encoberto. A B S T R A C T The aim of this study was to compare the results of soil heat flow, in the surface and depth, found by sensors soil heat flux and by harmonic method, in castor crop . On days without rainfall, the small amounts of water in the soil decreased its thermal diffusivity, causing a higher energy accumulation in the soil and consequently an increase at a temperature on the layers nearest the surface. The main differences between the measured and estimated values occurred at times of intense sunlight, especially on days when the sky was obscured by clouds. The presence of vegetation covering the soil directly influenced the values measured and modeled. Estimates both in depth and to the soil surface proved very satisfactory, both in clear sky conditions as for overcast days. Key-Words: Harmonic Method, Soil temperature, soil heat flux plates.
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50

Gustafson, Stephen, Kyungkeun Kang, and Tai-Peng Tsai. "Schrödinger flow near harmonic maps." Communications on Pure and Applied Mathematics 60, no. 4 (2007): 463–99. http://dx.doi.org/10.1002/cpa.20143.

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