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Volume 33, Issue 3
Higher Order Dissipative-Dispersive System and Application

Samer Israwi

DOI: 10.4208/jpde.v33.n3.6

J. Part. Diff. Eq., 33 (2020), pp. 261-274.

Published online: 2020-06

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  • Abstract

In this paper, a generalized nonlinear dissipative and dispersive equation with time and space-dependent coefficients is considered. We show that the control of the higher order term is possible by using an adequate weight function to define the energy. The existence and uniqueness of solutions are obtained via a Picard iterative method. As an application to this general Theorem, we prove the well-posedness of the Camassa-Holm type equation.

  • Keywords

Cauchy problem, Euler system, dispersive wave equation, Camassa-Holm equation.

  • AMS Subject Headings

35C07, 47G30, 35L05, 35A01

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

s.israwi@ul.edu.lb (Samer Israwi)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-33-261, author = {Israwi , Samer}, title = {Higher Order Dissipative-Dispersive System and Application}, journal = {Journal of Partial Differential Equations}, year = {2020}, volume = {33}, number = {3}, pages = {261--274}, abstract = {

In this paper, a generalized nonlinear dissipative and dispersive equation with time and space-dependent coefficients is considered. We show that the control of the higher order term is possible by using an adequate weight function to define the energy. The existence and uniqueness of solutions are obtained via a Picard iterative method. As an application to this general Theorem, we prove the well-posedness of the Camassa-Holm type equation.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v33.n3.6}, url = {http://global-sci.org/intro/article_detail/jpde/17074.html} }
TY - JOUR T1 - Higher Order Dissipative-Dispersive System and Application AU - Israwi , Samer JO - Journal of Partial Differential Equations VL - 3 SP - 261 EP - 274 PY - 2020 DA - 2020/06 SN - 33 DO - http://doi.org/10.4208/jpde.v33.n3.6 UR - https://global-sci.org/intro/article_detail/jpde/17074.html KW - Cauchy problem, Euler system, dispersive wave equation, Camassa-Holm equation. AB -

In this paper, a generalized nonlinear dissipative and dispersive equation with time and space-dependent coefficients is considered. We show that the control of the higher order term is possible by using an adequate weight function to define the energy. The existence and uniqueness of solutions are obtained via a Picard iterative method. As an application to this general Theorem, we prove the well-posedness of the Camassa-Holm type equation.

Samer Israwi. (2020). Higher Order Dissipative-Dispersive System and Application. Journal of Partial Differential Equations. 33 (3). 261-274. doi:10.4208/jpde.v33.n3.6
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