Evolution Problems with Nonlinear Nonlocal Boundary Conditions

被引：11

作者：

Benedetti, Irene ^{[1
]}

Taddei, Valentina ^{[2
]}

Vaeth, Martin ^{[3
]}

机构：

[1] Univ Perugia, Dept Math & Comp Sci, I-06123 Perugia, Italy

[2] Univ Modena & Reggio Emilia, Dept Phys Math & Comp Sci, I-41125 Modena, Italy

[3] Free Univ Berlin, Dept Math WE1, D-14195 Berlin, Germany

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2013年 / 25卷 / 02期

关键词：

Nonlinear boundary condition; Nonlocal boundary condition; Function triple degree; Nonlinear Fredholm map; Semilinear partial differential equation; Nonuniqueness; Profile-preserving growth; Age-population model; EQUATIONS; THEOREM;

D O I：

10.1007/s10884-013-9303-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：477 / 503

页数：27

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