Sriskandasingam, Mayuran; Sun, Shu-Ming; Zhang, Bing-Yu Non-homogeneous boundary value problems of the Kawahara equation posed on a finite interval. (English) Zbl 1504.35455 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 227, Article ID 113158, 28 p. (2023). Reviewer: Piotr Biler (Wrocław) MSC: 35Q53 35A01 35A02 35B65 35G05 PDFBibTeX XMLCite \textit{M. Sriskandasingam} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 227, Article ID 113158, 28 p. (2023; Zbl 1504.35455) Full Text: DOI
Li, Shenghao; Chen, Min; Yang, Xin; Zhang, Bing-Yu Lower regularity solutions of the non-homogeneous boundary-value problem for a higher order Boussinesq equation in a quarter plane. (English) Zbl 1489.35208 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 221, Article ID 112893, 29 p. (2022). MSC: 35Q35 35Q53 76B03 76B15 PDFBibTeX XMLCite \textit{S. Li} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 221, Article ID 112893, 29 p. (2022; Zbl 1489.35208) Full Text: DOI arXiv
Sun, Shu-Ming; Yang, Xin; Zhang, Bing-Yu; Zhong, Ning Kato smoothing properties of a class of nonlinear dispersive wave equations on a periodic domain. (English) Zbl 1468.35031 ESAIM, Control Optim. Calc. Var. 27, Paper No. 12, 27 p. (2021). MSC: 35B65 35Q53 35G25 35K45 PDFBibTeX XMLCite \textit{S.-M. Sun} et al., ESAIM, Control Optim. Calc. Var. 27, Paper No. 12, 27 p. (2021; Zbl 1468.35031) Full Text: DOI
Li, Shenghao; Chen, Min; Zhang, Bing-yu Low regularity solutions of non-homogeneous boundary value problems of a higher order Boussinesq equation in a quarter plane. (English) Zbl 1462.35300 J. Math. Anal. Appl. 492, No. 1, Article ID 124406, 35 p. (2020). MSC: 35Q35 35Q31 35Q53 76B15 PDFBibTeX XMLCite \textit{S. Li} et al., J. Math. Anal. Appl. 492, No. 1, Article ID 124406, 35 p. (2020; Zbl 1462.35300) Full Text: DOI arXiv
Cerpa, Eduardo; Montoya, Cristhian; Zhang, Bingyu Local exact controllability to the trajectories of the Korteweg-de Vries-Burgers equation on a bounded domain with mixed boundary conditions. (English) Zbl 1434.35151 J. Differ. Equations 268, No. 9, 4945-4972 (2020). MSC: 35Q53 93C20 93B05 76B15 PDFBibTeX XMLCite \textit{E. Cerpa} et al., J. Differ. Equations 268, No. 9, 4945--4972 (2020; Zbl 1434.35151) Full Text: DOI arXiv
Capistrano-Filho, Roberto A.; Sun, Shu-Ming; Zhang, Bing-Yu Initial boundary value problem for Korteweg-de Vries equation: a review and open problems. (English) Zbl 1431.35149 São Paulo J. Math. Sci. 13, No. 2, 402-417 (2019). MSC: 35Q53 35Q35 53C35 35A01 35A02 PDFBibTeX XMLCite \textit{R. A. Capistrano-Filho} et al., São Paulo J. Math. Sci. 13, No. 2, 402--417 (2019; Zbl 1431.35149) Full Text: DOI arXiv
Zhao, Xiangqing; Zhang, Bing-Yu Non-homogeneous boundary value problems of the fifth-order KdV equations on a bounded interval. (English) Zbl 1404.35399 J. Math. Anal. Appl. 470, No. 1, 251-278 (2019). MSC: 35Q53 47H10 44A10 PDFBibTeX XMLCite \textit{X. Zhao} and \textit{B.-Y. Zhang}, J. Math. Anal. Appl. 470, No. 1, 251--278 (2019; Zbl 1404.35399) Full Text: DOI
Capistrano-Filho, Roberto A.; Sun, Shuming; Zhang, Bing-Yu General boundary value problems of the Korteweg-de Vries equation on a bounded domain. (English) Zbl 1420.35307 Math. Control Relat. Fields 8, No. 3-4, 583-605 (2018). MSC: 35Q53 35Q35 53C35 PDFBibTeX XMLCite \textit{R. A. Capistrano-Filho} et al., Math. Control Relat. Fields 8, No. 3--4, 583--605 (2018; Zbl 1420.35307) Full Text: DOI arXiv
Li, Shenghao; Chen, Min; Zhang, Bing-Yu A non-homogeneous boundary value problem of the sixth order Boussinesq equation in a quarter plane. (English) Zbl 1397.35257 Discrete Contin. Dyn. Syst. 38, No. 5, 2505-2525 (2018). MSC: 35Q53 35Q55 35Q35 PDFBibTeX XMLCite \textit{S. Li} et al., Discrete Contin. Dyn. Syst. 38, No. 5, 2505--2525 (2018; Zbl 1397.35257) Full Text: DOI
Caicedo, Miguel Andres; Capistrano Filho, Roberto; Zhang, Bing-Yu Neumann boundary controllability of the Korteweg-de Vries equation on a bounded domain. (English) Zbl 1382.35255 SIAM J. Control Optim. 55, No. 6, 3503-3532 (2017). Reviewer: Piotr Biler (Wrocław) MSC: 35Q53 93B05 93D15 37K10 PDFBibTeX XMLCite \textit{M. A. Caicedo} et al., SIAM J. Control Optim. 55, No. 6, 3503--3532 (2017; Zbl 1382.35255) Full Text: DOI arXiv
Caicedo, Miguel Andres; Zhang, Bing-Yu Well-posedness of a nonlinear boundary value problem for the Korteweg-de Vries equation on a bounded domain. (English) Zbl 1388.35170 J. Math. Anal. Appl. 448, No. 2, 797-814 (2017). MSC: 35Q53 35B30 PDFBibTeX XMLCite \textit{M. A. Caicedo} and \textit{B.-Y. Zhang}, J. Math. Anal. Appl. 448, No. 2, 797--814 (2017; Zbl 1388.35170) Full Text: DOI
Wang, Chengqiang; Zhang, Bingyu The rapid stabilization of the Korteweg-de Vries equation on a finite interval. (Chinese. English summary) Zbl 1499.93065 Sci. Sin., Math. 46, No. 10, 1507-1532 (2016). MSC: 93D15 93D23 93C20 35Q53 PDFBibTeX XMLCite \textit{C. Wang} and \textit{B. Zhang}, Sci. Sin., Math. 46, No. 10, 1507--1532 (2016; Zbl 1499.93065) Full Text: DOI
Li, Shenghao; Rivas, Ivonne; Zhang, Bingyu A nonhomogeneous boundary value problem for the Boussinesq equation on a bounded domain. (English) Zbl 1374.35350 J. Math. Study 49, No. 3, 238-258 (2016). MSC: 35Q53 PDFBibTeX XMLCite \textit{S. Li} et al., J. Math. Study 49, No. 3, 238--258 (2016; Zbl 1374.35350) Full Text: DOI Link
Zhao, Xiangqing; Zhang, Bing-Yu Global controllability and stabilizability of Kawahara equation on a periodic domain. (English) Zbl 1322.93022 Math. Control Relat. Fields 5, No. 2, 335-358 (2015). MSC: 93B05 93D20 35Q53 PDFBibTeX XMLCite \textit{X. Zhao} and \textit{B.-Y. Zhang}, Math. Control Relat. Fields 5, No. 2, 335--358 (2015; Zbl 1322.93022) Full Text: DOI
Zhao, Xiangqing; Zhang, Bing-Yu Boundary smoothing properties of the Kawahara equation posed on the finite domain. (English) Zbl 1304.35626 J. Math. Anal. Appl. 417, No. 2, 519-536 (2014). MSC: 35Q53 44A10 35B65 35C05 PDFBibTeX XMLCite \textit{X. Zhao} and \textit{B.-Y. Zhang}, J. Math. Anal. Appl. 417, No. 2, 519--536 (2014; Zbl 1304.35626) Full Text: DOI
Jia, Chaohua; Rivas, Ivonne; Zhang, Bing-Yu Lower regularity solutions of a class of non-homogeneous boundary value problems of the Korteweg-de Vries equation on a finite domain. (English) Zbl 1291.35289 Adv. Differ. Equ. 19, No. 5-6, 559-584 (2014). MSC: 35Q53 35Q35 35B65 44A10 35B35 PDFBibTeX XMLCite \textit{C. Jia} et al., Adv. Differ. Equ. 19, No. 5--6, 559--584 (2014; Zbl 1291.35289) Full Text: Euclid
Cerpa, Eduardo; Rivas, Ivonne; Zhang, Bing-Yu Boundary controllability of the Korteweg-de Vries equation on a bounded domain. (English) Zbl 1275.93018 SIAM J. Control Optim. 51, No. 4, 2976-3010 (2013). MSC: 93B05 35Q53 93C10 PDFBibTeX XMLCite \textit{E. Cerpa} et al., SIAM J. Control Optim. 51, No. 4, 2976--3010 (2013; Zbl 1275.93018) Full Text: DOI arXiv Link
Rosier, Lionel; Zhang, Bing-Yu Unique continuation property and control for the Benjamin-Bona-Mahony equation on a periodic domain. (English) Zbl 1256.35122 J. Differ. Equations 254, No. 1, 141-178 (2013). MSC: 35Q53 93B05 93D15 PDFBibTeX XMLCite \textit{L. Rosier} and \textit{B.-Y. Zhang}, J. Differ. Equations 254, No. 1, 141--178 (2013; Zbl 1256.35122) Full Text: DOI arXiv
Zhang, Bing-Yu; Zhao, Xiangqing Control and stabilization of the Kawahara equation on a periodic domain. (English) Zbl 1266.93021 Commun. Inf. Syst. 12, No. 1, 77-95 (2012). MSC: 93B05 93D15 35Q53 PDFBibTeX XMLCite \textit{B.-Y. Zhang} and \textit{X. Zhao}, Commun. Inf. Syst. 12, No. 1, 77--95 (2012; Zbl 1266.93021) Full Text: DOI
Jia, Chaohua; Zhang, Bing-Yu Boundary stabilization of the Korteweg-de Vries equation and the Korteweg-de Vries-Burgers equation. (English) Zbl 1234.35225 Acta Appl. Math. 118, No. 1, 25-47 (2012). MSC: 35Q53 35B44 93C20 93D15 PDFBibTeX XMLCite \textit{C. Jia} and \textit{B.-Y. Zhang}, Acta Appl. Math. 118, No. 1, 25--47 (2012; Zbl 1234.35225) Full Text: DOI
Rivas, Ivonne; Usman, Muhammad; Zhang, Bing-Yu Global well-posedness and asymptotic behavior of a class of initial-boundary-value problem of the Korteweg-de Vries equation on a finite domain. (English) Zbl 1219.35251 Math. Control Relat. Fields 1, No. 1, 61-81 (2011). MSC: 35Q53 35Q35 35S15 PDFBibTeX XMLCite \textit{I. Rivas} et al., Math. Control Relat. Fields 1, No. 1, 61--81 (2011; Zbl 1219.35251) Full Text: DOI arXiv
Bona, J. L.; Chen, H.; Sun, S.-M.; Zhang, B.-Y. Approximating initial-value problems with two-point boundary-value problems: BBM-equation. (English) Zbl 1218.35203 Bull. Iran. Math. Soc. 36, No. 1, 1-25 (2010). MSC: 35Q53 76B03 76B15 45G10 65M99 PDFBibTeX XMLCite \textit{J. L. Bona} et al., Bull. Iran. Math. Soc. 36, No. 1, 1--25 (2010; Zbl 1218.35203)
Kramer, Eugene F.; Zhang, Bingyu Nonhomogeneous boundary value problems for the Korteweg-de Vries equation on a bounded domain. (English) Zbl 1202.35229 J. Syst. Sci. Complex. 23, No. 3, 499-526 (2010). MSC: 35Q53 35A01 35A02 PDFBibTeX XMLCite \textit{E. F. Kramer} and \textit{B. Zhang}, J. Syst. Sci. Complex. 23, No. 3, 499--526 (2010; Zbl 1202.35229) Full Text: DOI Link
Khanal, Netra; Wu, Jiahong; Yuan, Juan-Ming; Zhang, Bing-Yu Complex-valued Burgers and KdV-Burgers equations. (English) Zbl 1193.35192 J. Nonlinear Sci. 20, No. 3, 341-360 (2010). MSC: 35Q53 35B35 35B65 76D03 76M40 PDFBibTeX XMLCite \textit{N. Khanal} et al., J. Nonlinear Sci. 20, No. 3, 341--360 (2010; Zbl 1193.35192) Full Text: DOI arXiv
Laurent, Camille; Rosier, Lionel; Zhang, Bing-Yu Control and stabilization of the Korteweg-de Vries equation on a periodic domain. (English) Zbl 1213.93015 Commun. Partial Differ. Equations 35, No. 4, 707-744 (2010). MSC: 93B05 93D15 35Q53 93D20 PDFBibTeX XMLCite \textit{C. Laurent} et al., Commun. Partial Differ. Equations 35, No. 4, 707--744 (2010; Zbl 1213.93015) Full Text: DOI arXiv
Usman, Muhammad; Zhang, Bing-Yu Forced oscillations of the Korteweg-de Vries equation on a bounded domain and their stability. (English) Zbl 1187.35226 Discrete Contin. Dyn. Syst. 26, No. 4, 1509-1523 (2010). MSC: 35Q53 37K10 35B05 35B35 37K45 PDFBibTeX XMLCite \textit{M. Usman} and \textit{B.-Y. Zhang}, Discrete Contin. Dyn. Syst. 26, No. 4, 1509--1523 (2010; Zbl 1187.35226) Full Text: DOI
Rosier, Lionel; Zhang, Bing-Yu Control and stabilization of the Korteweg-de Vries equation: recent progresses. (English) Zbl 1300.93091 J. Syst. Sci. Complex. 22, No. 4, 647-682 (2009). MSC: 93C20 35Q53 93B05 93D99 PDFBibTeX XMLCite \textit{L. Rosier} and \textit{B.-Y. Zhang}, J. Syst. Sci. Complex. 22, No. 4, 647--682 (2009; Zbl 1300.93091) Full Text: DOI
Rosier, Lionel; Zhang, Bing-Yu Local exact controllability and stabilizability of the nonlinear Schrödinger equation on a bounded interval. (English) Zbl 1194.93026 SIAM J. Control Optim. 48, No. 2, 972-992 (2009). MSC: 93B05 93D15 35Q53 93D20 PDFBibTeX XMLCite \textit{L. Rosier} and \textit{B.-Y. Zhang}, SIAM J. Control Optim. 48, No. 2, 972--992 (2009; Zbl 1194.93026) Full Text: DOI
Bona, Jerry L.; Sun, Shu Ming; Zhang, Bing-Yu A non-homogeneous boundary-value problem for the Korteweg-de Vries equation posed on a finite domain. II. (English) Zbl 1181.35228 J. Differ. Equations 247, No. 9, 2558-2596 (2009). MSC: 35Q53 35A01 35A02 35B45 PDFBibTeX XMLCite \textit{J. L. Bona} et al., J. Differ. Equations 247, No. 9, 2558--2596 (2009; Zbl 1181.35228) Full Text: DOI
Bona, Jerry L.; Sun, S. M.; Zhang, Bing-Yu Non-homogeneous boundary value problems for the Korteweg-de Vries and the Korteweg-de Vries-Burgers equations in a quarter plane. (English) Zbl 1157.35090 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 25, No. 6, 1145-1185 (2008). MSC: 35Q53 35D05 35D10 PDFBibTeX XMLCite \textit{J. L. Bona} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 25, No. 6, 1145--1185 (2008; Zbl 1157.35090) Full Text: DOI EuDML
Usman, Muhammad; Zhang, Bingyu Forced oscillations of a class of nonlinear dispersive wave equations and their stability. (English) Zbl 1125.93027 J. Syst. Sci. Complex. 20, No. 2, 284-292 (2007). MSC: 93C10 93C20 35Q53 93D99 35B10 PDFBibTeX XMLCite \textit{M. Usman} and \textit{B. Zhang}, J. Syst. Sci. Complex. 20, No. 2, 284--292 (2007; Zbl 1125.93027) Full Text: DOI
Bona, Jerry L.; Chen, Hongqiu; Sun, Shu-Ming; Zhang, Bing-Yu Comparison of quarter-plane and two-point boundary value problems: the KdV-equation. (English) Zbl 1123.35052 Discrete Contin. Dyn. Syst., Ser. B 7, No. 3, 465-495 (2007). Reviewer: Igor Andrianov (Köln) MSC: 35Q53 76B03 PDFBibTeX XMLCite \textit{J. L. Bona} et al., Discrete Contin. Dyn. Syst., Ser. B 7, No. 3, 465--495 (2007; Zbl 1123.35052) Full Text: DOI
Rosier, Lionel; Zhang, Bing-Yu Global stabilization of the generalized Korteweg-de Vries equation posed on a finite domain. (English) Zbl 1116.35108 SIAM J. Control Optim. 45, No. 3, 927-956 (2006). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 35Q53 35B35 93D15 PDFBibTeX XMLCite \textit{L. Rosier} and \textit{B.-Y. Zhang}, SIAM J. Control Optim. 45, No. 3, 927--956 (2006; Zbl 1116.35108) Full Text: DOI Link
Bona, Jerry L.; Sun, S. M.; Zhang, Bingyu Boundary smoothing properties of the Korteweg-de Vries equation in a quarter plane and applications. (English) Zbl 1152.35099 Dyn. Partial Differ. Equ. 3, No. 1, 1-69 (2006). Reviewer: Igor Andrianov (Köln) MSC: 35Q53 PDFBibTeX XMLCite \textit{J. L. Bona} et al., Dyn. Partial Differ. Equ. 3, No. 1, 1--69 (2006; Zbl 1152.35099) Full Text: DOI
Bona, Jerry L.; Chen, Hongqiu; Sun, Shu Ming; Zhang, B.-Y. Comparison of quarter-plane and two-point boundary value problems: the BBM-equation. (English) Zbl 1088.35057 Discrete Contin. Dyn. Syst. 13, No. 4, 921-940 (2005). Reviewer: Qin Mengzhao (Beijing) MSC: 35Q53 76B15 76B03 45G10 65M99 PDFBibTeX XMLCite \textit{J. L. Bona} et al., Discrete Contin. Dyn. Syst. 13, No. 4, 921--940 (2005; Zbl 1088.35057) Full Text: DOI
Bona, Jerry L.; Sun, S. M.; Zhang, Bing-Yu A non-homogeneous boundary-value problem for the Korteweg-de Vries equation in a quarter plane. (English) Zbl 0988.35141 Trans. Am. Math. Soc. 354, No. 2, 427-490 (2002). Reviewer: G.F.Roach (Glasgow) MSC: 35Q53 76B03 76B15 PDFBibTeX XMLCite \textit{J. L. Bona} et al., Trans. Am. Math. Soc. 354, No. 2, 427--490 (2002; Zbl 0988.35141) Full Text: DOI
Zhang, Bing-Yu Forced oscillation of the Korteweg-de Vries-Burgers equation and its stability. (English) Zbl 0982.93044 Chen, Goong (ed.) et al., Control of nonlinear distributed parameter systems. Partly proceedings of the conference advances in control of nonlinear distributed parameter systems, Texas A & M Univ., College Station, TX, USA. Dedicated to Prof. David L. Russell on the occasion of his 60th birthday. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 218, 337-357 (2001). Reviewer: Vadim Komkov (Florida) MSC: 93C20 35B10 35Q53 PDFBibTeX XMLCite \textit{B.-Y. Zhang}, Lect. Notes Pure Appl. Math. 218, 337--357 (2001; Zbl 0982.93044)
Gay, William; Zhang, Bing-Yu; Zhong, Ning Computability of solutions of the Korteweg-de Vries equation. (English) Zbl 0970.03047 Math. Log. Q. 47, No. 1, 93-110 (2001). Reviewer: Zheng Xizhong (Cottbus) MSC: 03F60 35Q53 03D80 PDFBibTeX XMLCite \textit{W. Gay} et al., Math. Log. Q. 47, No. 1, 93--110 (2001; Zbl 0970.03047) Full Text: DOI
Zhang, Bing-Yu Exact boundary controllability of the Korteweg–de Vries equation. (English) Zbl 0930.35160 SIAM J. Control Optimization 37, No. 2, 543-565 (1999). Reviewer: S.P.Banks (Sheffield) MSC: 35Q53 35B37 35K60 93C20 PDFBibTeX XMLCite \textit{B.-Y. Zhang}, SIAM J. Control Optim. 37, No. 2, 543--565 (1999; Zbl 0930.35160) Full Text: DOI
Russell, David L.; Zhang, Bing-Yu Exact controllability and stabilizability of the Korteweg-de Vries equation. (English) Zbl 0862.93035 Trans. Am. Math. Soc. 348, No. 9, 3643-3672 (1996). Reviewer: T.Nambu (Kobe) MSC: 93C20 35K60 93D15 35Q53 PDFBibTeX XMLCite \textit{D. L. Russell} and \textit{B.-Y. Zhang}, Trans. Am. Math. Soc. 348, No. 9, 3643--3672 (1996; Zbl 0862.93035) Full Text: DOI
Bona, Jerry L.; Zhang, Bing-Yu The initial-value problem for the forced Korteweg-de Vries equation. (English) Zbl 0865.35114 Proc. R. Soc. Edinb., Sect. A 126, No. 3, 571-598 (1996). Reviewer: B.A.Malomed (Tel Aviv) MSC: 35Q53 35B65 35B10 PDFBibTeX XMLCite \textit{J. L. Bona} and \textit{B.-Y. Zhang}, Proc. R. Soc. Edinb., Sect. A, Math. 126, No. 3, 571--598 (1996; Zbl 0865.35114) Full Text: DOI
Russell, David L.; Zhang, Bing-Yu Smoothing and decay properties of solutions of the Korteweg-de Vries equation on a periodic domain with point dissipation. (English) Zbl 0845.35111 J. Math. Anal. Appl. 190, No. 2, 449-488 (1995). Reviewer: G.Jumarie (Montreal) MSC: 35Q53 35B40 35B65 PDFBibTeX XMLCite \textit{D. L. Russell} and \textit{B.-Y. Zhang}, J. Math. Anal. Appl. 190, No. 2, 449--488 (1995; Zbl 0845.35111) Full Text: DOI
Zhang, Bing-Yu Taylor series expansion for solutions of the Korteweg-de Vries equation with respect to their initial values. (English) Zbl 0835.35130 J. Funct. Anal. 129, No. 2, 293-324 (1995). Reviewer: O.Titow (Berlin) MSC: 35Q53 35C10 PDFBibTeX XMLCite \textit{B.-Y. Zhang}, J. Funct. Anal. 129, No. 2, 293--324 (1995; Zbl 0835.35130) Full Text: DOI
Zhang, Bing-Yu A remark on the Cauchy problem for the Korteweg-de Vries equation on a periodic domain. (English) Zbl 0826.35114 Differ. Integral Equ. 8, No. 5, 1191-1204 (1995). MSC: 35Q53 30B50 PDFBibTeX XMLCite \textit{B.-Y. Zhang}, Differ. Integral Equ. 8, No. 5, 1191--1204 (1995; Zbl 0826.35114)
Komornik, Vilmos; Russell, David L.; Zhang, Bing-Yu Stabilisation de l’équation de Korteweg-de Vries. (Stabilization of the Korteweg-de Vries equation). (French. Abridged English version) Zbl 0742.35058 C. R. Acad. Sci., Paris, Sér. I 312, No. 11, 841-843 (1991). MSC: 35Q53 93D15 PDFBibTeX XMLCite \textit{V. Komornik} et al., C. R. Acad. Sci., Paris, Sér. I 312, No. 11, 841--843 (1991; Zbl 0742.35058)