Advances in Differential Equations

Quasilinear parabolic problems via maximal regularity

Herbert Amann

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We use maximal $L_p$~regularity to study quasilinear parabolic evolution equations. In contrast to all previous work we only assume that the nonlinearities are defined on the space in which the solution is sought for. It is shown that there exists a unique maximal solution depending continuously on all data, and criteria for global existence are given as well. These general results possess numerous applications, some of which will be discussed in separate publications.

Article information

Adv. Differential Equations, Volume 10, Number 10 (2005), 1081-1110.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34G20: Nonlinear equations [See also 47Hxx, 47Jxx]
Secondary: 35B35: Stability 35K90: Abstract parabolic equations 47H20: Semigroups of nonlinear operators [See also 37L05, 47J35, 54H15, 58D07] 47N20: Applications to differential and integral equations


Amann, Herbert. Quasilinear parabolic problems via maximal regularity. Adv. Differential Equations 10 (2005), no. 10, 1081--1110.

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