@Article{JPDE-20-114, author = {}, title = {Asymptotic Behavior of Global Classical Solutions to a Kind of Mixed Initial-boundary Value Problem}, journal = {Journal of Partial Differential Equations}, year = {2007}, volume = {20}, number = {2}, pages = {114--130}, abstract = {

We study the asymptotic behavior of global classical solutions to a kind of mixed initial-boundary value problem for quasilinear hyperbolic systems. Based on the existence results on the global classical solutions given by Li and Wang in [1] and employing the method of Kong and Yang in [2], we prove that, when t tends to infinity, the solution approaches a combination of C¹ travelling wave solutions at the algebraic rate (1+t)^{-μ}, provided that the initial data decay at the rate (1+x)^{-(1+μ)} as x tends to +∞ and the boundary data decay at the rate (1+t)^{-(1+μ)} as t tends to +∞, where μ is a positive constant.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5297.html} }