Taiwanese Journal of Mathematics

Attraction Property of Admissible Integral Manifolds and Applications to Fisher-Kolmogorov Model

Nguyen Thieu Huy, Trinh Viet Duoc, and Dinh Xuan Khanh

Full-text: Open access

Abstract

In this paper we investigate the attraction property of an unstable manifold of admissible classes for solutions to the semi-linear evolution equation of the form $u(t) = U(t,s) u(s) + \int_s^t U(t, \xi) f(\xi, u(\xi)) \, d\xi$. These manifolds are constituted by trajectories of the solutions belonging to admissible function spaces which contain wide classes of function spaces like $L_p$-spaces, the Lorentz spaces $L_{p, q}$ and many other function spaces occurring in interpolation theory. We then apply our abstract results to study Fisher-Kolmogorov model with time-dependent environmental capacity.

Article information

Source
Taiwanese J. Math., Volume 20, Number 2 (2016), 365-385.

Dates
First available in Project Euclid: 1 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1498874445

Digital Object Identifier
doi:10.11650/tjm.20.2016.6357

Mathematical Reviews number (MathSciNet)
MR3481389

Zentralblatt MATH identifier
1357.34083

Subjects
Primary: 34C45: Invariant manifolds 34G20: Nonlinear equations [See also 47Hxx, 47Jxx] 35B40: Asymptotic behavior of solutions 37D10: Invariant manifold theory

Keywords
exponential dichotomy admissibility of function spaces integral manifolds of admissible classes Fisher-Kolmogorov model with time-dependent environmental capacity

Citation

Thieu Huy, Nguyen; Viet Duoc, Trinh; Xuan Khanh, Dinh. Attraction Property of Admissible Integral Manifolds and Applications to Fisher-Kolmogorov Model. Taiwanese J. Math. 20 (2016), no. 2, 365--385. doi:10.11650/tjm.20.2016.6357. https://projecteuclid.org/euclid.twjm/1498874445


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