Nonlocal diffusion second order partial differential equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:262

Article

Benedetti, I.¹  Loi, N. V.²  Malaguti, L.³  Taddei, V.⁴ 

[1] Univ Perugia, Dept Math & Comp Sci, I-06100 Perugia, Italy

[2] PetroVietNam Univ, Fac Fundamental Sci, Hanoi, Vietnam

[3] Univ Modena & Reggio Emilia, Dept Sci & Methods Engn, Modena, Italy

[4] Univ Modena & Reggio Emilia, Dept Phys Informat & Math, Modena, Italy

关键词: Nonlocal diffusion;    Second order integro-partial differential equation;    Approximation solvability method;    Periodic solution;    Nonlocal condition;    Degree theory;   

DOI  :  10.1016/j.jde.2016.10.019

来源: Elsevier

【 摘 要 】

The paper deals with a second order integro-partial differential equation in lam with a nonlocal, degenerate diffusion term. Nonlocal conditions, such as the Cauchy multipoint and the weighted mean value problem, are investigated. The existence of periodic solutions is also studied. The dynamic is transformed into an abstract setting and the results come from an approximation solvability method. It combines a Schauder degree argument with an Hartman-type inequality and it involves a Scorza-Dragoni type result. The corn pact embedding of a suitable Sobolev space in the corresponding Lebesgue space is the unique amount of compactness which is needed in this discussion. The solutions are located in bounded sets and they are limits of functions with values in finitely dimensional spaces. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free