1.主要课题
1. 国家自然科学基金重点项目,非线性可积系统的几何结构和奇性分析(11631007),2017-2021,参与;
2. 国家自然科学基金面上项目,具有不光滑孤子解非线性色散波方程的奇性解和全局解(11471259), 2015-2018, 主持,已结题;
3. 国家自然科学基金青年项目,具有尖峰孤子解浅水波系统的整体解和爆破解(11001219), 2011-2013, 主持,已结题;
4. 陕西省杰出青年科学基金项目, 非线性可积系统的爆破解和整体解(2020JC-37) ,2020-2022,主持;
5. 陕西省自然科学基础研究计划面上项目, 具有不光滑孤子解的可积系统解的定性性质研究(2019JM-007),2019-2020, 主持;
6. 陕西省自然科学基础研究计划青年项目, 具有尖峰孤子解的推广Camassa-Holm方程解的定性性质(2014JQ1002),2014-2016,已结题;
7. 陕西省教育厅自然科学专项,一类浅水波系统解的性质研究(2010JK860),2010-2012,主持,已结题.
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[1] Ying Fu*, Haiquan Wang, A note on the solution map for the periodic multi-dimensional Camassa-Holm-type system, Monatshefte für Mathematik, (2021). https://doi.org/10.1007/s00605-021-01615-8.
[2] Haiquan Wang*,Gezi Chong, Lili Wu, A note on the solution map for the two-component Novikov system in Besov spaces, Journal of Evolution Equations , 2021, 21(2): 1809-1843 .
[3] Haiquan Wang*, Yu Guo, A note on the initial value problem for a higher-order Camassa–Holm equation, Mathematische Nachrichten , 2020, accepted .
[4] Yingying Li, Ying Fu, Changzheng Qu*, The two-component $\mu$- Camassa--Holm system with peaked solutions, Discrete and Continuous Dynamical Systems - Series A, 2020, 40(10): 5929-5954.
[5] Haiquan Wang*, Gezi Chong, On the initial value problem for the two-coupled Camassa–Holm system in Besov spaces, Monatshefte für Mathematik , 2020, 193(2): 479-505.
[6] Changzheng Qu, Ying Fu*, Curvature blow-up for the higher-order Camassa-Holm equations, Journal of Dynamics and Differential Equations, 2020, 32(4): 1901-1939.
[7] Changzheng Qu*, Ying Fu, On Cauchy problem and peakons of a two-component Novikov system, SCIENCE CHINA Mathematics, 2020,63(10): 1965-1996.
[8] Haiquan Wang, Ying Fu*, A note on the Cauchy problem for the periodic two-component Novikov system, Applicable Analysis, 2020, 99(6): 1042-1065.
[9] Ying Fu*, Juanjuan Gao, On the support of solutions to the fifth-order Kadomtsev–Petviashvili II equation in three-dimensional space, Applicable Analysis, 2018, 97(16): 2794-2817.
[10] Ying Fu, Changzheng Qu*, Well-posedness and wave breaking of the degenerate Novikov equation, J. Differential Equations,2017, 263(8): 4634-4657.
[11] Haiquan Wang, Ying Fu*, Non-uniform dependence on initial data for the two-component Novikov system, Journal of Mathematical Physics, 2017, 58: 021502,22pp.
[12] Haiquan Wang, Ying Fu*, Non-uniform dependence on initial data for the modified \mu-Camassa-Holm equation, Journal of Differential Equations, 2016, 261(11):6099-6124.
[13] Ying Fu, A note on the Cauchy problem of a modified Camassa-Holm equation with cubic nonlinearity, Discrete Continuous Dynam. Systems, 2015, 35(5): 2011-2039.
[14] Changzheng Qu, Ying Fu, Yue Liu, Blow-up solutions and peakons to a generalized $\mu$-Camassa-Holm integrable equation, Comm. Math. Phys., 2014,331 (1):375-416.
[15] Changzheng Qu, Ying Fu, Yue Liu, Well-posedness, wave breaking and peakons for a modified $\mu$-Camassa-Holm equation, Journal of Functional Analysis, 2014,266(2): 433-477.
[16] Ying Fu, Guilong Gui, Yue Liu, On the Cauchy problem for the integrable modified Camassa-Holm equation with cubic nonlinearity, J. Differential Equations, 2013, 255:1905-1938.
[17] Ying Fu, Yue Liu, Changzheng Qu. On the blow-up structure for the generalized periodic Camassa-Holm and Degasperis-Procesi equations, Journal of Functional Analysis, 2012, 262: 3125-3158.
[18] Ying Fu, Changzheng Qu, Unique continuation and persistence properties of solutions of the 2-component Degasperis-procesi equations, Acta Math. Sci. Ser. B Engl. Ed., 2012, 32: 652-662.
[19] Ying Fu, Yue Liu, Changzheng Qu , Well-posedness and blow-up solution for a modified two-component periodic Camassa-Holm system with peakons, Math. Ann., 2010, 348(2): 415-448.
[20] Ying Fu, Changzheng Qu, Yichen Ma, Well-posedness and blow-up phenomena for the interacting system of the Camassa-Holm and Degasperis-Procesi equations, Discrete Continuous Dynam. Systems, 2010, 27(3): 1025-1035.
[21] Changzheng Qu,Ying Fu, On a new three-component Camassa-Holm equation with peakons, Commun. Theor. Phys., 2010, 53(2):223-230.
[22] Ying Fu, Changzheng Qu . Well posedness and blow-up solution for a new coupled Camassa-Holm equations with peakons, Journal of Mathematical Physics, 2009, 50: 012906, 25pp.
[23] Ying Fu, Changzheng Qu. Unique continuation property for the Generalized Davey-Stewartson System in Rn, 数学进展, 2013, 42(1): 95-105.
[24] Ying Fu, Changzheng Qu, Yichen Ma. On the unique continuation property for a coupled Schrödinger-KdV equation,数学进展,2010, 39(2): 169-178.
Latest update: September 29, 2021.
3.获奖情况
科研获奖:
1. 屈长征,张顺利,黄晴,康静,付英等,非线性偏微分方程的对称、不变量和几何可积性,获2010年度陕西省科学技术奖一等奖。
2. 题为“Well-posedness and blow-up solution for a modified two-component periodic Camassa-Holm system with peakons”的论文获得陕西省数学会2011年青年优秀论文一等奖。
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1.窦霁虹,郭真华,付英,常微分方程课程获批2019年陕西省线上线下混合式一流本科课程;
2.窦霁虹,付英,王丽真,刘俊荣,刘小川,赵婷婷,常微分方程课程获批2014年陕西省升级改造精品资源共享课程;
3.窦霁虹,付英,王丽真,刘俊荣,刘小川,赵婷婷,常微分方程教学团队获批2014年度陕西本科高校省级教学团队;
4.窦霁虹,付英,刘俊荣,赵婷婷,数学建模思想在“常微分方程”课程教学中融入与实践获2015年度威廉希尔体育官方网站教学成果奖一等奖。