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Dissipative and weakly--dissipative regimes in nearly--integrable mappings
A concept of solution and numerical experiments for forward-backward diffusion equations
1. | Dipartimento di Matematica, Università di Roma 'Tor Vergata', 00133, Roma |
2. | Dipartimento di Matematica Pura e Applicata, Università de L’Aquila, I-67100 L’Aquila, Italy |
3. | Dipartimento di Matematica Pura e Applicata, Università de L'Aquila, I-67100 L'Aquila |
[1] |
Fabio Paronetto. Elliptic approximation of forward-backward parabolic equations. Communications on Pure and Applied Analysis, 2020, 19 (2) : 1017-1036. doi: 10.3934/cpaa.2020047 |
[2] |
Flavia Smarrazzo, Alberto Tesei. Entropy solutions of forward-backward parabolic equations with Devonshire free energy. Networks and Heterogeneous Media, 2012, 7 (4) : 941-966. doi: 10.3934/nhm.2012.7.941 |
[3] |
Yufeng Shi, Tianxiao Wang, Jiongmin Yong. Optimal control problems of forward-backward stochastic Volterra integral equations. Mathematical Control and Related Fields, 2015, 5 (3) : 613-649. doi: 10.3934/mcrf.2015.5.613 |
[4] |
Jiongmin Yong. Forward-backward evolution equations and applications. Mathematical Control and Related Fields, 2016, 6 (4) : 653-704. doi: 10.3934/mcrf.2016019 |
[5] |
Flavia Smarrazzo, Andrea Terracina. Sobolev approximation for two-phase solutions of forward-backward parabolic problems. Discrete and Continuous Dynamical Systems, 2013, 33 (4) : 1657-1697. doi: 10.3934/dcds.2013.33.1657 |
[6] |
Xin Chen, Ana Bela Cruzeiro. Stochastic geodesics and forward-backward stochastic differential equations on Lie groups. Conference Publications, 2013, 2013 (special) : 115-121. doi: 10.3934/proc.2013.2013.115 |
[7] |
Jiongmin Yong. Forward-backward stochastic differential equations: Initiation, development and beyond. Numerical Algebra, Control and Optimization, 2022 doi: 10.3934/naco.2022011 |
[8] |
Peng Gao. Carleman estimates for forward and backward stochastic fourth order Schrödinger equations and their applications. Evolution Equations and Control Theory, 2018, 7 (3) : 465-499. doi: 10.3934/eect.2018023 |
[9] |
Fabio Paronetto. A Harnack type inequality and a maximum principle for an elliptic-parabolic and forward-backward parabolic De Giorgi class. Discrete and Continuous Dynamical Systems - S, 2017, 10 (4) : 853-866. doi: 10.3934/dcdss.2017043 |
[10] |
Lianzhang Bao, Zhengfang Zhou. Traveling wave in backward and forward parabolic equations from population dynamics. Discrete and Continuous Dynamical Systems - B, 2014, 19 (6) : 1507-1522. doi: 10.3934/dcdsb.2014.19.1507 |
[11] |
Xiao Ding, Deren Han. A modification of the forward-backward splitting method for maximal monotone mappings. Numerical Algebra, Control and Optimization, 2013, 3 (2) : 295-307. doi: 10.3934/naco.2013.3.295 |
[12] |
Andrés Contreras, Juan Peypouquet. Forward-backward approximation of nonlinear semigroups in finite and infinite horizon. Communications on Pure and Applied Analysis, 2021, 20 (5) : 1893-1906. doi: 10.3934/cpaa.2021051 |
[13] |
Kaitong Hu, Zhenjie Ren, Nizar Touzi. On path-dependent multidimensional forward-backward SDEs. Numerical Algebra, Control and Optimization, 2022 doi: 10.3934/naco.2022010 |
[14] |
Jie Xiong, Shuaiqi Zhang, Yi Zhuang. A partially observed non-zero sum differential game of forward-backward stochastic differential equations and its application in finance. Mathematical Control and Related Fields, 2019, 9 (2) : 257-276. doi: 10.3934/mcrf.2019013 |
[15] |
Z. B. Ibrahim, N. A. A. Mohd Nasir, K. I. Othman, N. Zainuddin. Adaptive order of block backward differentiation formulas for stiff ODEs. Numerical Algebra, Control and Optimization, 2017, 7 (1) : 95-106. doi: 10.3934/naco.2017006 |
[16] |
Andrea L. Bertozzi, Ning Ju, Hsiang-Wei Lu. A biharmonic-modified forward time stepping method for fourth order nonlinear diffusion equations. Discrete and Continuous Dynamical Systems, 2011, 29 (4) : 1367-1391. doi: 10.3934/dcds.2011.29.1367 |
[17] |
Dariusz Borkowski. Forward and backward filtering based on backward stochastic differential equations. Inverse Problems and Imaging, 2016, 10 (2) : 305-325. doi: 10.3934/ipi.2016002 |
[18] |
Adel Chala, Dahbia Hafayed. On stochastic maximum principle for risk-sensitive of fully coupled forward-backward stochastic control of mean-field type with application. Evolution Equations and Control Theory, 2020, 9 (3) : 817-843. doi: 10.3934/eect.2020035 |
[19] |
Jasmina Djordjević, Svetlana Janković. Reflected backward stochastic differential equations with perturbations. Discrete and Continuous Dynamical Systems, 2018, 38 (4) : 1833-1848. doi: 10.3934/dcds.2018075 |
[20] |
Zongming Guo, Long Wei. A fourth order elliptic equation with a singular nonlinearity. Communications on Pure and Applied Analysis, 2014, 13 (6) : 2493-2508. doi: 10.3934/cpaa.2014.13.2493 |
2020 Impact Factor: 1.392
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