Almost global strong solutions to quasilinear dissipative evolution equations

Abstract

The author proves a global existence result for strong solutions to the quasilinear dissipative hyperbolic equation (1.1) below, corresponding to initial values and source terms of arbitrary size, provided that the hyperbolicity parameter ε is sufficiently small. This implies a corresponding global existence result for the reduced quasilinear parabolic equation (1.4) below.

Keywords

Quasilinear evolution equation / A priori estimates / Global existence / Small parameter

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