Journal of Dynamics and Differential Equations

, Volume 25, Issue 2, pp 477–503

Evolution Problems with Nonlinear Nonlocal Boundary Conditions

Article

DOI: 10.1007/s10884-013-9303-8

Cite this article as:
Benedetti, I., Taddei, V. & Väth, M. J Dyn Diff Equat (2013) 25: 477. doi:10.1007/s10884-013-9303-8

Abstract

We provide a new approach to obtain solutions of evolution equations with nonlinear and nonlocal in time boundary conditions. Both, compact and noncompact semigroups are considered. As an example we show a “principle of huge growth”: every control of a reaction-diffusion system necessarily leads to a profile preserving nonlinear huge growth for an appropriate initial value condition. As another example we apply the approach with noncompact semigroups also to a class of age-population models, based on a hyperbolic conservation law.

Keywords

Nonlinear boundary conditionNonlocal boundary conditionFunction triple degreeNonlinear Fredholm mapSemilinear partial differential equationNonuniquenessProfile-preserving growthAge-population model

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Irene Benedetti
    • 1
  • Valentina Taddei
    • 2
  • Martin Väth
    • 3
  1. 1.Department of Mathematics and Computer ScienceUniversity of PerugiaPerugiaItaly
  2. 2.Department of Physical, Mathematical and Computer SciencesUniversity of Modena and Reggio EmiliaModenaItaly
  3. 3.Department of Mathematics (WE1)Free University of BerlinBerlinGermany