The paper deals with a second order integro-partial differential equation in RnRn 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 compact 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.

Nonlocal diffusion second order partial differential equations / Benedetti, Irene; Loi, Nguyen Van; Malaguti, Luisa; Taddei, Valentina. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - ELETTRONICO. - 262:3(2017), pp. 1499-1523. [10.1016/j.jde.2016.10.019]

Nonlocal diffusion second order partial differential equations

MALAGUTI, Luisa;TADDEI, Valentina
2017

Abstract

The paper deals with a second order integro-partial differential equation in RnRn 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 compact 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.
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Nonlocal diffusion second order partial differential equations / Benedetti, Irene; Loi, Nguyen Van; Malaguti, Luisa; Taddei, Valentina. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - ELETTRONICO. - 262:3(2017), pp. 1499-1523. [10.1016/j.jde.2016.10.019]
Benedetti, Irene; Loi, Nguyen Van; Malaguti, Luisa; Taddei, Valentina
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1114450
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