an:03927425
Zbl 0579.34037
Schiaffino, Andrea; Tesei, Alberto
Linearized stability results in continuous interpolation spaces
EN
Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 11, 281-301 (1984).
00149462
1984
j
34D20 34G10 47D03
interpolation techniques; asymptotic stability; stationary solution; quasilinear Cauchy problem; nonlinear diffusion problems
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.
R.Nagel