Global existence of small data solutions for wave models with sub-exponential propagation speed

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• 作者：Tang Bao Ngoc Bui^a ; ^b ; ^{buitangngockstn@yahoo.com" class="auth_mail" title="E-mail the corresponding author} ; Michael Reissig^a ; ^{reissig@math.tu-freiberg.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35L15 ; 35L05 ; 35L71
• 刊名：Nonlinear Analysis
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：129
• 期：Complete
• 页码：173-188
• 全文大小：759 K

文摘

In the paper (Bui and Reissig, 2015) we explained that it is reasonable to divide the study of global existence of small data solutions to semi-linear classical damped wave models with time-dependent speed of propagation, time-dependent dissipation and power nonlinearity into two cases. The super-exponential case was treated in Bui and Reissig (2015). The present paper is devoted to the sub-exponential case. Both cases arise from a different influence of the interplay of time-dependent coefficients on the critical exponent. Here we only sketch differences to the approach for the super-exponential case. These differences appear in handling the nonlinearity. The corresponding Matsumura type estimates for a family of linear Cauchy problems depending on a parameter coincide in both cases (see Bui and Reissig (2014, 2015)).