Global existence of small solutions to a class of nonlinear evolution equations. (English) Zbl 0576.35023

The author studies the global behaviour of solutions to the initial value problem for certain quasilinear equations which are perturbations of ”dissipative” linear ones. He shows that for sufficiently small nonlinear perturbations, global solutions exist which behave asymptotically like the solutions of the associated linear problem.
Reviewer: A.D.Osborne


35G25 Initial value problems for nonlinear higher-order PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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