Milani, Albert Global existence via singular perturbations for quasilinear evolution equations. (English) Zbl 0868.35008 Adv. Math. Sci. Appl. 6, No. 2, 419-444 (1996). The paper deals with the initial value problems \[ \varepsilon u_{tt}+ u_t- \sum^n_{i,j=1} a_{ij}(Du)D_iD_ju= f,\;x\in\mathbb{R}^n,\;u(0,x)=u_0\quad\text{for }\varepsilon\geq 0,\;u_t(0,x)= u_1\quad\text{for }\varepsilon>0. \] The global in time smooth solutions to the above problems are established and the estimates of the difference \(u^\varepsilon- u^0\), which give the singular convergence of the solutions if \(\varepsilon\) tends to 0, are proved. Reviewer: M.Kopáčková (Praha) Cited in 8 Documents MSC: 35B25 Singular perturbations in context of PDEs 35L70 Second-order nonlinear hyperbolic equations 35B40 Asymptotic behavior of solutions to PDEs Keywords:quasilinear wave equation; singular convergence PDF BibTeX XML Cite \textit{A. Milani}, Adv. Math. Sci. Appl. 6, No. 2, 419--444 (1996; Zbl 0868.35008) OpenURL