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Small data solutions for semilinear wave equations with effective damping
Analysis of the accelerated weighted ensemble methodology
1.  Mechanical Engineering Department, Stanford University, CA, United States 
2.  Computer Science and Engineering, University of Notre Dame, IN, United States, United States 
3.  Mechanical Engineering Department and Institute for Computational and Mathematical Engineering, Stanford University, CA, United States 
References:
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Jiongmin Yong. Remarks on some short rate term structure models. Journal of Industrial & Management Optimization, 2006, 2 (2) : 119134. doi: 10.3934/jimo.2006.2.119 
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LeongKwan Li, Sally Shao. Convergence analysis of the weighted state space search algorithm for recurrent neural networks. Numerical Algebra, Control & Optimization, 2014, 4 (3) : 193207. doi: 10.3934/naco.2014.4.193 
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C. Cortázar, Marta GarcíaHuidobro. On the uniqueness of ground state solutions of a semilinear equation containing a weighted Laplacian. Communications on Pure & Applied Analysis, 2006, 5 (1) : 7184. doi: 10.3934/cpaa.2006.5.71 
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DongMei Zhu, WaiKi Ching, Robert J. Elliott, TakKuen Siu, Lianmin Zhang. Hidden Markov models with threshold effects and their applications to oil price forecasting. Journal of Industrial & Management Optimization, 2017, 13 (2) : 757773. doi: 10.3934/jimo.2016045 
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Youcef Amirat, Kamel Hamdache. Steady state solutions of ferrofluid flow models. Communications on Pure & Applied Analysis, 2016, 15 (6) : 23292355. doi: 10.3934/cpaa.2016039 
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Yu Yang, Dongmei Xiao. Influence of latent period and nonlinear incidence rate on the dynamics of SIRS epidemiological models. Discrete & Continuous Dynamical Systems  B, 2010, 13 (1) : 195211. doi: 10.3934/dcdsb.2010.13.195 
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Cruz VargasDeLeón, Alberto d'Onofrio. Global stability of infectious disease models with contact rate as a function of prevalence index. Mathematical Biosciences & Engineering, 2017, 14 (4) : 10191033. doi: 10.3934/mbe.2017053 
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Sebastian Reich, Seoleun Shin. On the consistency of ensemble transform filter formulations. Journal of Computational Dynamics, 2014, 1 (1) : 177189. doi: 10.3934/jcd.2014.1.177 
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Badal Joshi. A detailed balanced reaction network is sufficient but not necessary for its Markov chain to be detailed balanced. Discrete & Continuous Dynamical Systems  B, 2015, 20 (4) : 10771105. doi: 10.3934/dcdsb.2015.20.1077 
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Samira Boussaïd, Danielle Hilhorst, Thanh Nam Nguyen. Convergence to steady state for the solutions of a nonlocal reactiondiffusion equation. Evolution Equations & Control Theory, 2015, 4 (1) : 3959. doi: 10.3934/eect.2015.4.39 
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LeongKwan Li, Sally Shao, K. F. Cedric Yiu. Nonlinear dynamical system modeling via recurrent neural networks and a weighted state space search algorithm. Journal of Industrial & Management Optimization, 2011, 7 (2) : 385400. doi: 10.3934/jimo.2011.7.385 
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Virginia GonzálezVélez, Amparo Gil, Iván Quesada. Minimal state models for ionic channels involved in glucagon secretion. Mathematical Biosciences & Engineering, 2010, 7 (4) : 793807. doi: 10.3934/mbe.2010.7.793 
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W. Y. Tan, L.J. Zhang, C.W. Chen. Stochastic modeling of carcinogenesis: State space models and estimation of parameters. Discrete & Continuous Dynamical Systems  B, 2004, 4 (1) : 297322. doi: 10.3934/dcdsb.2004.4.297 
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ChihYuan Chen, ShinHwa Wang, KuoChih Hung. Sshaped bifurcation curves for a combustion problem with general arrhenius reactionrate laws. Communications on Pure & Applied Analysis, 2014, 13 (6) : 25892608. doi: 10.3934/cpaa.2014.13.2589 
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SeungYeal Ha, Jaeseung Lee, Zhuchun Li. Emergence of local synchronization in an ensemble of heterogeneous Kuramoto oscillators. Networks & Heterogeneous Media, 2017, 12 (1) : 124. doi: 10.3934/nhm.2017001 
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