Nikolai Nefedov

Address: Lomonosov Moscow State University,GSP-1, Leninskie Gory, Moscow, 119992, Russia

E-mail: nefedov@phys.msu.ru

University: Faculty of Physics, M.V. Lomonosov Moscow State University

Publications:

Nefedov N. N., Recke L., Schneider K. R.

Asymptotic stability via the Krein–Rutman theorem for singularly perturbed parabolic periodic Dirichlet problems
2010, vol. 15, nos. 2-3, pp. 382-389

Abstract

We consider singularly perturbed semilinear parabolic periodic problems and assume the existence of a family of solutions. We present an approach to establish the exponential asymptotic stability of these solutions by means of a special class of lower and upper solutions. The proof is based on a corollary of the Krein–Rutman theorem.

Keywords: singularly perturbed parabolic Dirichlet problems, exponential asymptotic stability, Krein–Rutman theorem, lower and upper solutions

Citation: Nefedov N. N., Recke L., Schneider K. R., Asymptotic stability via the Krein–Rutman theorem for singularly perturbed parabolic periodic Dirichlet problems, Regular and Chaotic Dynamics, 2010, vol. 15, nos. 2-3, pp. 382-389

DOI:10.1134/S1560354710020231

Back to the list