Initial boundary value problem for generalized Zakharov equations

Shujun You; Boling Guo; Xiaoqi Ning

Applications of Mathematics (2012)

  • Volume: 57, Issue: 6, page 581-599
  • ISSN: 0862-7940

Abstract

top
This paper considers the existence and uniqueness of the solution to the initial boundary value problem for a class of generalized Zakharov equations in ( 2 + 1 ) dimensions, and proves the global existence of the solution to the problem by a priori integral estimates and the Galerkin method.

How to cite

top

You, Shujun, Guo, Boling, and Ning, Xiaoqi. "Initial boundary value problem for generalized Zakharov equations." Applications of Mathematics 57.6 (2012): 581-599. <http://eudml.org/doc/246495>.

@article{You2012,
abstract = {This paper considers the existence and uniqueness of the solution to the initial boundary value problem for a class of generalized Zakharov equations in $(2+1)$ dimensions, and proves the global existence of the solution to the problem by a priori integral estimates and the Galerkin method.},
author = {You, Shujun, Guo, Boling, Ning, Xiaoqi},
journal = {Applications of Mathematics},
keywords = {global solutions; modified Zakharov equations; Galerkin method; modified Zakharov equations; global solution; Galerkin method},
language = {eng},
number = {6},
pages = {581-599},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Initial boundary value problem for generalized Zakharov equations},
url = {http://eudml.org/doc/246495},
volume = {57},
year = {2012},
}

TY - JOUR
AU - You, Shujun
AU - Guo, Boling
AU - Ning, Xiaoqi
TI - Initial boundary value problem for generalized Zakharov equations
JO - Applications of Mathematics
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 6
SP - 581
EP - 599
AB - This paper considers the existence and uniqueness of the solution to the initial boundary value problem for a class of generalized Zakharov equations in $(2+1)$ dimensions, and proves the global existence of the solution to the problem by a priori integral estimates and the Galerkin method.
LA - eng
KW - global solutions; modified Zakharov equations; Galerkin method; modified Zakharov equations; global solution; Galerkin method
UR - http://eudml.org/doc/246495
ER -

References

top
  1. Garcia, L. G., Haas, F., Oliveira, L. P. L. de, Goedert, J., 10.1063/1.1819935, Phys. Plasmas 12 (2005). (2005) DOI10.1063/1.1819935
  2. Guo, B., Zhang, J., Pu, X., 10.1016/j.jmaa.2009.10.045, J. Math. Anal. Appl. 365 (2010), 238-253. (2010) Zbl1185.35275MR2585095DOI10.1016/j.jmaa.2009.10.045
  3. Holmer, J., Local ill-posedness of the 1D Zakharov system, Electron. J. Differ. Equ. 24 (2007), 1-24. (2007) Zbl1115.35124MR2299578
  4. Linares, F., Matheus, C., Well-posedness for the 1D Zakharov-Rubenchik system, Adv. Differ. Equ. 14 (2009), 261-288. (2009) Zbl1165.35448MR2493563
  5. Linares, F., Saut, J.-C., 10.3934/dcds.2009.24.547, Discrete Cont. Dyn. Syst. 24 (2009), 547-565. (2009) Zbl1170.35086MR2486590DOI10.3934/dcds.2009.24.547
  6. Lions, J.-L., Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod/Gauthier-Villars Paris/Paris (1969), French. (1969) Zbl0189.40603MR0259693
  7. Masmoudi, N., Nakanishi, K., 10.1142/S0219891605000683, J. Hyperbolic Differ. Equ. 2 (2005), 975-1008. (2005) Zbl1089.35070MR2195989DOI10.1142/S0219891605000683
  8. Masmoudi, N., Nakanishi, K., 10.1007/s00222-008-0110-5, Invent. Math. 172 (2008), 535-583. (2008) Zbl1143.35090MR2393080DOI10.1007/s00222-008-0110-5
  9. Pecher, H., 10.1016/j.jmaa.2008.01.035, J. Math. Anal. Appl. 342 (2008), 1440-1454. (2008) Zbl1140.35307MR2445287DOI10.1016/j.jmaa.2008.01.035
  10. You, S.-J., 10.1016/j.na.2009.01.234, Nonlinear Anal., Theory Methods Appl. 71 (2009), 3571-3584. (2009) Zbl1183.35247MR2532737DOI10.1016/j.na.2009.01.234
  11. Zakharov, V. E., Collapse of Langmuir waves, Sov. Phys. JETP 35 (1972), 908-914. (1972) 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.