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Volume 24, Issue 4
Well- and Ill-posedness Issues for a Class of 2D Wave Equation with Exponential Growth

Olfa Mahouachi & Tarek Saanouni

DOI: 10.4208/jpde.v24.n4.7

J. Part. Diff. Eq., 24 (2011), pp. 361-384.

Published online: 2011-11

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  • Abstract

Extending the previous work [1], we establish well-posedness results for a more general class of semilinear wave equations with exponential growth. First, we investigate the well-posedness in the energy space. Then, we prove the propagation of the regularity in the Sobolev spaces H^s(R^2) with s ≥ 1. Finally, an ill-posedness result is obtained in H^s(R^2) for s < 1.

  • Keywords

Nonlinear wave equation well-posedness ill-posedness Moser-Trudinger inequality finite speed of propagation

  • AMS Subject Headings

35L70 35B40 35B44 47J30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-24-361, author = {Olfa Mahouachi and Tarek Saanouni }, title = {Well- and Ill-posedness Issues for a Class of 2D Wave Equation with Exponential Growth}, journal = {Journal of Partial Differential Equations}, year = {2011}, volume = {24}, number = {4}, pages = {361--384}, abstract = {

Extending the previous work [1], we establish well-posedness results for a more general class of semilinear wave equations with exponential growth. First, we investigate the well-posedness in the energy space. Then, we prove the propagation of the regularity in the Sobolev spaces H^s(R^2) with s ≥ 1. Finally, an ill-posedness result is obtained in H^s(R^2) for s < 1.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v24.n4.7}, url = {http://global-sci.org/intro/article_detail/jpde/5217.html} }
TY - JOUR T1 - Well- and Ill-posedness Issues for a Class of 2D Wave Equation with Exponential Growth AU - Olfa Mahouachi & Tarek Saanouni JO - Journal of Partial Differential Equations VL - 4 SP - 361 EP - 384 PY - 2011 DA - 2011/11 SN - 24 DO - http://doi.org/10.4208/jpde.v24.n4.7 UR - https://global-sci.org/intro/article_detail/jpde/5217.html KW - Nonlinear wave equation KW - well-posedness KW - ill-posedness KW - Moser-Trudinger inequality KW - finite speed of propagation AB -

Extending the previous work [1], we establish well-posedness results for a more general class of semilinear wave equations with exponential growth. First, we investigate the well-posedness in the energy space. Then, we prove the propagation of the regularity in the Sobolev spaces H^s(R^2) with s ≥ 1. Finally, an ill-posedness result is obtained in H^s(R^2) for s < 1.

Olfa Mahouachi and Tarek Saanouni . (2011). Well- and Ill-posedness Issues for a Class of 2D Wave Equation with Exponential Growth. Journal of Partial Differential Equations. 24 (4). 361-384. doi:10.4208/jpde.v24.n4.7
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