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Breakdown of $C^1$ solution to the Cauchy problem for quasilinear hyperbolic systems with characteristics with constant multiplicity
Analysis and numerical approximation of a class of twoway diffusions
1.  Department of Mathematics, Hong Kong Baptist University, Hong Kong 
2.  Department of Statistics, Oxford University, 1 South Parks Road, Oxford, OX1 3TG, United Kingdom 
[1] 
Yufeng Shi, Tianxiao Wang, Jiongmin Yong. Optimal control problems of forwardbackward stochastic Volterra integral equations. Mathematical Control & Related Fields, 2015, 5 (3) : 613649. doi: 10.3934/mcrf.2015.5.613 
[2] 
Xin Chen, Ana Bela Cruzeiro. Stochastic geodesics and forwardbackward stochastic differential equations on Lie groups. Conference Publications, 2013, 2013 (special) : 115121. doi: 10.3934/proc.2013.2013.115 
[3] 
Jiongmin Yong. Forwardbackward evolution equations and applications. Mathematical Control & Related Fields, 2016, 6 (4) : 653704. doi: 10.3934/mcrf.2016019 
[4] 
Fabio Paronetto. Elliptic approximation of forwardbackward parabolic equations. Communications on Pure & Applied Analysis, 2020, 19 (2) : 10171036. doi: 10.3934/cpaa.2020047 
[5] 
Yaozhong Hu, Yanghui Liu, David Nualart. Taylor schemes for rough differential equations and fractional diffusions. Discrete & Continuous Dynamical Systems  B, 2016, 21 (9) : 31153162. doi: 10.3934/dcdsb.2016090 
[6] 
G. Bellettini, Giorgio Fusco, Nicola Guglielmi. A concept of solution and numerical experiments for forwardbackward diffusion equations. Discrete & Continuous Dynamical Systems  A, 2006, 16 (4) : 783842. doi: 10.3934/dcds.2006.16.783 
[7] 
Flavia Smarrazzo, Alberto Tesei. Entropy solutions of forwardbackward parabolic equations with Devonshire free energy. Networks & Heterogeneous Media, 2012, 7 (4) : 941966. doi: 10.3934/nhm.2012.7.941 
[8] 
Jie Xiong, Shuaiqi Zhang, Yi Zhuang. A partially observed nonzero sum differential game of forwardbackward stochastic differential equations and its application in finance. Mathematical Control & Related Fields, 2019, 9 (2) : 257276. doi: 10.3934/mcrf.2019013 
[9] 
Dariusz Borkowski. Forward and backward filtering based on backward stochastic differential equations. Inverse Problems & Imaging, 2016, 10 (2) : 305325. doi: 10.3934/ipi.2016002 
[10] 
Shaokuan Chen, Shanjian Tang. Semilinear backward stochastic integral partial differential equations driven by a Brownian motion and a Poisson point process. Mathematical Control & Related Fields, 2015, 5 (3) : 401434. doi: 10.3934/mcrf.2015.5.401 
[11] 
Flavia Smarrazzo, Andrea Terracina. Sobolev approximation for twophase solutions of forwardbackward parabolic problems. Discrete & Continuous Dynamical Systems  A, 2013, 33 (4) : 16571697. doi: 10.3934/dcds.2013.33.1657 
[12] 
Cécile AppertRolland, Pierre Degond, Sébastien Motsch. Twoway multilane traffic model for pedestrians in corridors. Networks & Heterogeneous Media, 2011, 6 (3) : 351381. doi: 10.3934/nhm.2011.6.351 
[13] 
Xiao Ding, Deren Han. A modification of the forwardbackward splitting method for maximal monotone mappings. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 295307. doi: 10.3934/naco.2013.3.295 
[14] 
Lianzhang Bao, Zhengfang Zhou. Traveling wave in backward and forward parabolic equations from population dynamics. Discrete & Continuous Dynamical Systems  B, 2014, 19 (6) : 15071522. doi: 10.3934/dcdsb.2014.19.1507 
[15] 
Onur Alp İlhan. Solvability of some partial integral equations in Hilbert space. Communications on Pure & Applied Analysis, 2008, 7 (4) : 837844. doi: 10.3934/cpaa.2008.7.837 
[16] 
Fabio Paronetto. A Harnack type inequality and a maximum principle for an ellipticparabolic and forwardbackward parabolic De Giorgi class. Discrete & Continuous Dynamical Systems  S, 2017, 10 (4) : 853866. doi: 10.3934/dcdss.2017043 
[17] 
Jasmina Djordjević, Svetlana Janković. Reflected backward stochastic differential equations with perturbations. Discrete & Continuous Dynamical Systems  A, 2018, 38 (4) : 18331848. doi: 10.3934/dcds.2018075 
[18] 
Jan A. Van Casteren. On backward stochastic differential equations in infinite dimensions. Discrete & Continuous Dynamical Systems  S, 2013, 6 (3) : 803824. doi: 10.3934/dcdss.2013.6.803 
[19] 
Shitao Liu, Roberto Triggiani. Determining damping and potential coefficients of an inverse problem for a system of two coupled hyperbolic equations. Part I: Global uniqueness. Conference Publications, 2011, 2011 (Special) : 10011014. doi: 10.3934/proc.2011.2011.1001 
[20] 
Yufeng Shi, Tianxiao Wang, Jiongmin Yong. Meanfield backward stochastic Volterra integral equations. Discrete & Continuous Dynamical Systems  B, 2013, 18 (7) : 19291967. doi: 10.3934/dcdsb.2013.18.1929 
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