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.
Evolution Problems with Nonlinear Nonlocal Boundary Conditions / Irene, Benedetti; Taddei, Valentina; Martin, Vath. - In: JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS. - ISSN 1040-7294. - STAMPA. - 25:(2013), pp. 477-503. [10.1007/s10884-013-9303-8]
Evolution Problems with Nonlinear Nonlocal Boundary Conditions
TADDEI, Valentina;
2013
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.
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