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Linearized stability results in continuous interpolation spaces. (English) Zbl 0579.34037
Using interpolation techniques the authors discuss the problem of how the asymptotic stability of a stationary solution of a quasilinear Cauchy problem \(\dot u(t)=Au(t)+\sigma (u(t)),\) \(u(0)=u_ 0\), in a Banach space E and for the nonlinearity \(\sigma\) :D(A)\(\to E\) can be derived from the stability of the linearization. An application to nonlinear diffusion problems is made.
Reviewer: R.Nagel

MSC:
34D20 Stability of solutions to ordinary differential equations
34G10 Linear differential equations in abstract spaces
47D03 Groups and semigroups of linear operators
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