Inertial manifolds for semi-linear parabolic equations in admissible spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:386

Article

Nguyen Thieu Huy

关键词: Generalized spectral gap conditions;    Semi-linear parabolic equations;    Admissibility of function spaces;    Inertial manifolds;    Lyapunov-Perron method;   

DOI  :  10.1016/j.jmaa.2011.08.051

来源: Elsevier

【 摘 要 】

We prove the existence of inertial manifolds for the solutions to the semi-linear parabolic equation du(t)/dt + Au(t) = f (t, u) when the partial differential operator A is positive definite and self-adjoint with a discrete spectrum having a sufficiently large distance between some two successive points of the spectrum, and the nonlinear forcing term f satisfies the phi-Lipschitz conditions on the domain D(A(0)). 0 <= theta < 1, i.e., parallel to f(t, x) - f (t. y)parallel to <= phi(t) parallel to A(0) (x - y) parallel to and parallel to f(t, x)parallel to phi(t)(1 + parallel to A(0) x parallel to) where phi(t) belongs to one of admissible function spaces containing wide classes of function spaces like L-p-spaces, the Lorentz spaces L-p,L-q and many other function spaces occurring in interpolation theory. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free