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Volume 22, Issue 1
On Global Smooth Solution of a Semi-linear System of Wave Equations in R3

Haigen Wu

J. Part. Diff. Eq., 22 (2009), pp. 74-96.

Published online: 2009-02

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  • Abstract

In this paper we consider the Cauchy problem for a semi-linear system of wave equations with Hamilton structure. We prove the existence of global smooth solution of the systemfor subcritical case by using conservation of energy and Strichartz's estimate. On the basis ofMorawetz-Poho\check{z}ev identity, we obtain the same result for the critical case.

  • Keywords

Critical subcritical Strichartz's estimate Lagrangian function Morawetz-Poho\check{z}ev identity Huygen's principle

  • AMS Subject Headings

35L05 35L15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-22-74, author = {Haigen Wu }, title = {On Global Smooth Solution of a Semi-linear System of Wave Equations in R3}, journal = {Journal of Partial Differential Equations}, year = {2009}, volume = {22}, number = {1}, pages = {74--96}, abstract = {

In this paper we consider the Cauchy problem for a semi-linear system of wave equations with Hamilton structure. We prove the existence of global smooth solution of the systemfor subcritical case by using conservation of energy and Strichartz's estimate. On the basis ofMorawetz-Poho\check{z}ev identity, we obtain the same result for the critical case.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5248.html} }
TY - JOUR T1 - On Global Smooth Solution of a Semi-linear System of Wave Equations in R3 AU - Haigen Wu JO - Journal of Partial Differential Equations VL - 1 SP - 74 EP - 96 PY - 2009 DA - 2009/02 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5248.html KW - Critical KW - subcritical KW - Strichartz's estimate KW - Lagrangian function KW - Morawetz-Poho\check{z}ev identity KW - Huygen's principle AB -

In this paper we consider the Cauchy problem for a semi-linear system of wave equations with Hamilton structure. We prove the existence of global smooth solution of the systemfor subcritical case by using conservation of energy and Strichartz's estimate. On the basis ofMorawetz-Poho\check{z}ev identity, we obtain the same result for the critical case.

Haigen Wu . (2009). On Global Smooth Solution of a Semi-linear System of Wave Equations in R3. Journal of Partial Differential Equations. 22 (1). 74-96. doi:
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