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Communications in Partial Differential Equations Volume 39, 2014 - Issue 12
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Original Articles

Norm Inflation and Ill-Posedness for the Degasperis-Procesi Equation

A. Alexandrou Himonas Department of Mathematics, University of Notre Dame, Notre Dame, Indiana, USACorrespondence[email protected]
,
Curtis Holliman Department of Mathematics, University of Notre Dame, Notre Dame, Indiana, USA
&
Katelyn Grayshan Department of Mathematics, University of Notre Dame, Notre Dame, Indiana, USA
Pages 2198-2215 | Received 17 Jun 2011, Accepted 02 Jul 2014, Published online: 16 Sep 2014

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Xijun Deng. (2022) Blow-up criteria for the generalized Degasperis–Procesi equation. Applicable Analysis 101:13, pages 4639-4649.
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Articles from other publishers (31)

Zaiyun Zhang, Zhenhai Liu & Youjun Deng. (2024) Global energy conservation solution for the family of Camassa–Holm type equation . Nonlinear Analysis: Real World Applications 78, pages 104093.
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Weipeng Zhu, Min Li & Jinlu Li. (2023) Ill-posedness for the two component Degasperis–Procesi equation in critical Besov space. Monatshefte für Mathematik 204:2, pages 395-407.
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Jinlu Li, Yanghai Yu & Weipeng Zhu. (2022) Ill-posedness for the Burgers equation in Sobolev spaces. Indian Journal of Pure and Applied Mathematics 55:1, pages 189-197.
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Nikolai V. Chemetov & Fernanda Cipriano. (2024) Weak solution for stochastic Degasperis-Procesi equation. Journal of Differential Equations 382, pages 1-49.
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Kexin Yan, Hao Wang & Ying Fu. (2023) Ill-posedness of the Cauchy problem for the $$\mu $$-Camassa–Holm-type equations. Journal of Evolution Equations 23:4.
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A. Alexandrou Himonas & Fangchi Yan. (2023) On Well-Posedness of Nonlocal Evolution Equations. Vietnam Journal of Mathematics 51:4, pages 811-844.
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Jinlu Li, Xing Wu, Yanghai Yu & Weipeng Zhu. (2023) Norm inflation and ill-posedness for the Fornberg–Whitham equation. Journal of Differential Equations 368, pages 301-316.
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J. L. Bona & F. B. Weissler. (2022) Blowup and ill-posedness for the complex, periodic KdV equation. Communications in Contemporary Mathematics 25:06.
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Lynnyngs K. Arruda, Nikolai V. Chemetov & Fernanda Cipriano. (2021) Solvability of the Stochastic Degasperis-Procesi Equation. Journal of Dynamics and Differential Equations 35:1, pages 523-542.
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Jinlu Li, Yanghai Yu & Weipeng Zhu. (2022) Well-posedness and continuity properties of the Degasperis-Procesi equation in critical Besov space. Monatshefte für Mathematik 200:2, pages 301-313.
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Hans Lundmark & Jacek Szmigielski. (2022) A view of the peakon world through the lens of approximation theory. Physica D: Nonlinear Phenomena 440, pages 133446.
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Aiyong Chen, Hao Yu & Xiaokai He. (2022) 2-Peakon Solutions and Non-uniqueness of the Fokas–Olver–Rosenau–Qiao Equation with Higher-Order Nonlinearity. Bulletin of the Malaysian Mathematical Sciences Society 45:6, pages 3401-3422.
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A. Alexandrou Himonas & Curtis Holliman. (2022) Instability and Nonuniqueness for the b-Novikov Equation. Journal of Nonlinear Science 32:4.
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Hao Yu, Aiyong Chen & Kelei Zhang. (2021) Construction of 2-Peakon Solutions and Nonuniqueness for a Generalized mCH Equation. Advances in Mathematical Physics 2021, pages 1-10.
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John Holmes & Rajan Puri. (2021) Non-uniqueness for the ab-family of equations. Journal of Mathematical Analysis and Applications 493:2, pages 124563.
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Emil Novruzov. (2021) Construction of peakon-antipeakon solutions and ill-posedness for the b-family of equations. Journal of Differential Equations 272, pages 544-559.
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Zaiyun Zhang, Zhenhai Liu, Youjun Deng, Chuangxia Huang, Shiyou Lin & Wen Zhu. (2020) Global well-posedness and infinite propagation speed for the N − abc family of Camassa–Holm type equation with both dissipation and dispersion . Journal of Mathematical Physics 61:7.
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Qiaoyi Hu & Zhijun Qiao. (2019) Global existence and propagation speed for a generalized Camassa–Holm model with both dissipation and dispersion. Journal of Evolution Equations 20:2, pages 403-419.
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A. Alexandrou Himonas & Curtis Holliman. (2019) Non-uniqueness for the Fokas–Olver–Rosenau–Qiao equation. Journal of Mathematical Analysis and Applications 470:1, pages 647-658.
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A. Alexandrou Himonas, Curtis Holliman & Carlos Kenig. (2018) Construction of 2-Peakon Solutions and Ill-Posedness for the Novikov Equation. SIAM Journal on Mathematical Analysis 50:3, pages 2968-3006.
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Felipe Linares, Gustavo Ponce & Derek L. Smith. (2016) On the regularity of solutions to a class of nonlinear dispersive equations. Mathematische Annalen 369:1-2, pages 797-837.
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Rafael F. Barostichi, A. Alexandrou Himonas & Gerson Petronilho. (2017) Global analyticity for a generalized Camassa–Holm equation and decay of the radius of spatial analyticity. Journal of Differential Equations 263:1, pages 732-764.
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Rafael F. Barostichi, A. Alexandrou Himonas & Gerson Petronilho. (2016) The power series method for nonlocal and nonlinear evolution equations. Journal of Mathematical Analysis and Applications 443:2, pages 834-847.
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A. Alexandrou Himonas, Katelyn Grayshan & Curtis Holliman. (2016) Ill-Posedness for the b-Family of Equations. Journal of Nonlinear Science 26:5, pages 1175-1190.
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A. Himonas & Dionyssios Mantzavinos. (2016) An 𝑎𝑏-family of equations with peakon traveling waves. Proceedings of the American Mathematical Society 144:9, pages 3797-3811.
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A. Alexandrou Himonas & Dionyssios Mantzavinos. (2016) The initial value problem for a Novikov system. Journal of Mathematical Physics 57:7.
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Yanggeng Fu, Zanping Yu & Jianhe Shen. (2016) Non-uniform dependence on initial data for the generalized Degasperis–Procesi equation on the line. International Journal of Mathematics 27:03, pages 1650026.
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A. Alexandrou Himonas & Dionyssios Mantzavinos. (2016) The Cauchy problem for a 4-parameter family of equations with peakon traveling waves. Nonlinear Analysis 133, pages 161-199.
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Rafael F. Barostichi, A. Alexandrou Himonas & Gerson Petronilho. (2016) Autonomous Ovsyannikov theorem and applications to nonlocal evolution equations and systems. Journal of Functional Analysis 270:1, pages 330-358.
Crossref
Rafael F. Barostichi, A. Alexandrou Himonas & Gerson Petronilho. 2015. Analysis and Geometry. Analysis and Geometry 59 68 .
A. Alexandrou Himonas & Ryan C. Thompson. (2014) Persistence properties and unique continuation for a generalized Camassa-Holm equation. Journal of Mathematical Physics 55:9.
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