Annals of Functional Analysis

Decay bounds for nonlocal evolution equations in Orlicz spaces

Uriel Kaufmann, Julio D. Rossi, and Raul Vidal

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We show decay bounds of the form

Rdϕ(u(x,t))dxCtμ for integrable and bounded solutions to the nonlocal evolution equation

ut(x,t)=RdJ(x,y)G(u(y,t)u(x,t))(u(y,t)u(x,t))dy+f(u(x,t)). Here G is a nonnegative and even function, and f verifies f(ξ)ξ0 for all ξ0. We remark that G is not assumed to be homogeneous. The function ϕ and the exponent μ depend on G via adequate hypotheses, while J is a nonnegative kernel satisfying suitable assumptions.

Article information

Ann. Funct. Anal., Volume 7, Number 2 (2016), 261-269.

Received: 13 March 2015
Accepted: 9 July 2015
First available in Project Euclid: 29 February 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47G10: Integral operators [See also 45P05]
Secondary: 47J35: Nonlinear evolution equations [See also 34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx, 37Lxx, 47H20, 58D25] 45G10: Other nonlinear integral equations

Orlicz space nonlocal diffusion energy methods


Kaufmann, Uriel; Rossi, Julio D.; Vidal, Raul. Decay bounds for nonlocal evolution equations in Orlicz spaces. Ann. Funct. Anal. 7 (2016), no. 2, 261--269. doi:10.1215/20088752-3475634.

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