Global existence via singular perturbations for quasilinear evolution equations. (English) Zbl 0868.35008

Milani, Albert

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)

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