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Nonlocal heat flows preserving the L^{2} energy
1.  Department of Mathematics, University of Texas at Austin, 1 University Station, C1200, Austin, TX 787121082 
2.  Department of Mathematics, New York University, 251 Mercer St. New York, NY 10012 
[1] 
Minbo Yang, Yanheng Ding. Existence of solutions for singularly perturbed Schrödinger equations with nonlocal part. Communications on Pure & Applied Analysis, 2013, 12 (2) : 771783. doi: 10.3934/cpaa.2013.12.771 
[2] 
Keisuke Matsuya, Tetsuji Tokihiro. Existence and nonexistence of global solutions for a discrete semilinear heat equation. Discrete & Continuous Dynamical Systems, 2011, 31 (1) : 209220. doi: 10.3934/dcds.2011.31.209 
[3] 
Ibrahima Faye, Emmanuel Frénod, Diaraf Seck. Singularly perturbed degenerated parabolic equations and application to seabed morphodynamics in tided environment. Discrete & Continuous Dynamical Systems, 2011, 29 (3) : 10011030. doi: 10.3934/dcds.2011.29.1001 
[4] 
C. Brändle, E. Chasseigne, Raúl Ferreira. Unbounded solutions of the nonlocal heat equation. Communications on Pure & Applied Analysis, 2011, 10 (6) : 16631686. doi: 10.3934/cpaa.2011.10.1663 
[5] 
Xie Li, Zhaoyin Xiang. Existence and nonexistence of local/global solutions for a nonhomogeneous heat equation. Communications on Pure & Applied Analysis, 2014, 13 (4) : 14651480. doi: 10.3934/cpaa.2014.13.1465 
[6] 
Peiying Chen. Existence and uniqueness of weak solutions for a class of nonlinear parabolic equations. Electronic Research Announcements, 2017, 24: 3852. doi: 10.3934/era.2017.24.005 
[7] 
Sergey Zelik. Asymptotic regularity of solutions of singularly perturbed damped wave equations with supercritical nonlinearities. Discrete & Continuous Dynamical Systems, 2004, 11 (2&3) : 351392. doi: 10.3934/dcds.2004.11.351 
[8] 
Shihui Zhu. Existence and uniqueness of global weak solutions of the CamassaHolm equation with a forcing. Discrete & Continuous Dynamical Systems, 2016, 36 (9) : 52015221. doi: 10.3934/dcds.2016026 
[9] 
Shijin Ding, Boling Guo, Junyu Lin, Ming Zeng. Global existence of weak solutions for LandauLifshitzMaxwell equations. Discrete & Continuous Dynamical Systems, 2007, 17 (4) : 867890. doi: 10.3934/dcds.2007.17.867 
[10] 
Zhengce Zhang, Yan Li. Global existence and gradient blowup of solutions for a semilinear parabolic equation with exponential source. Discrete & Continuous Dynamical Systems  B, 2014, 19 (9) : 30193029. doi: 10.3934/dcdsb.2014.19.3019 
[11] 
Michele Coti Zelati. Global and exponential attractors for the singularly perturbed extensible beam. Discrete & Continuous Dynamical Systems, 2009, 25 (3) : 10411060. doi: 10.3934/dcds.2009.25.1041 
[12] 
Daomin Cao, Norman E. Dancer, Ezzat S. Noussair, Shunsen Yan. On the existence and profile of multipeaked solutions to singularly perturbed semilinear Dirichlet problems. Discrete & Continuous Dynamical Systems, 1996, 2 (2) : 221236. doi: 10.3934/dcds.1996.2.221 
[13] 
Xiumei Deng, Jun Zhou. Global existence and blowup of solutions to a semilinear heat equation with singular potential and logarithmic nonlinearity. Communications on Pure & Applied Analysis, 2020, 19 (2) : 923939. doi: 10.3934/cpaa.2020042 
[14] 
Weichung Wang, TsungFang Wu, ChienHsiang Liu. On the multiple spike solutions for singularly perturbed elliptic systems. Discrete & Continuous Dynamical Systems  B, 2013, 18 (1) : 237258. doi: 10.3934/dcdsb.2013.18.237 
[15] 
Xiaoliang Li, Baiyu Liu. Finite time blowup and global solutions for a nonlocal parabolic equation with Hartree type nonlinearity. Communications on Pure & Applied Analysis, 2020, 19 (6) : 30933112. doi: 10.3934/cpaa.2020134 
[16] 
Antonio Greco, Antonio Iannizzotto. Existence and convexity of solutions of the fractional heat equation. Communications on Pure & Applied Analysis, 2017, 16 (6) : 22012226. doi: 10.3934/cpaa.2017109 
[17] 
Bernhard Ruf, P. N. Srikanth. Hopf fibration and singularly perturbed elliptic equations. Discrete & Continuous Dynamical Systems  S, 2014, 7 (4) : 823838. doi: 10.3934/dcdss.2014.7.823 
[18] 
Pavol Quittner. The decay of global solutions of a semilinear heat equation. Discrete & Continuous Dynamical Systems, 2008, 21 (1) : 307318. doi: 10.3934/dcds.2008.21.307 
[19] 
Rui Huang, Yifu Wang, Yuanyuan Ke. Existence of nontrivial nonnegative periodic solutions for a class of degenerate parabolic equations with nonlocal terms. Discrete & Continuous Dynamical Systems  B, 2005, 5 (4) : 10051014. doi: 10.3934/dcdsb.2005.5.1005 
[20] 
Fei Jiang, Song Jiang, Junpin Yin. Global weak solutions to the twodimensional NavierStokes equations of compressible heatconducting flows with symmetric data and forces. Discrete & Continuous Dynamical Systems, 2014, 34 (2) : 567587. doi: 10.3934/dcds.2014.34.567 
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