Evolution Problems with Nonlinear Nonlocal Boundary Conditions
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- Benedetti, I., Taddei, V. & Väth, M. J Dyn Diff Equat (2013) 25: 477. doi:10.1007/s10884-013-9303-8
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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.