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Bulletin of the Australian Mathematical Society Bulletin of the Australian Mathematical Society

Article contents

A NEW NONLOCAL NONLINEAR DIFFUSION EQUATION: THE ONE-DIMENSIONAL CASE

Part of: Parabolic equations and systems

Published online by Cambridge University Press:  05 May 2022

G. ALETTI Open the ORCID record for G. ALETTI[Opens in a new window] ,
A. BENFENATI Open the ORCID record for A. BENFENATI[Opens in a new window]  and
G. NALDI Open the ORCID record for G. NALDI[Opens in a new window]
G. ALETTI
Affiliation:
Environmental Science and Policy Department, Università degli Studi di Milano, 20133Milan, Italy e-mail: giacomo.aletti@unimi.it
A. BENFENATI
Affiliation:
Environmental Science and Policy Department, Università degli Studi di Milano, 20133Milan, Italy e-mail: alessandro.benfenati@unimi.it
G. NALDI*
Affiliation:
Advanced Applied Mathematical and Statistical Sciences Center, Università degli Studi di Milano, 20133Milan, Italy
*
e-mail: giovanni.naldi@unimi.it
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Abstract

We prove a result on the existence and uniqueness of the solution of a new feature-preserving nonlinear nonlocal diffusion equation for signal denoising for the one-dimensional case. The partial differential equation is based on a novel diffusivity coefficient that uses a nonlocal automatically detected parameter related to the local bounded variation and the local oscillating pattern of the noisy input signal.

Keywords

nonlocal diffusion equationfixed point methodsignal denoising

MSC classification

Primary: 35K59: Quasilinear parabolic equations
Secondary: 35K20: Initial-boundary value problems for second-order parabolic equations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 7
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The three authors are members of the Italian Group GNCS of the Italian Institute ‘Istituto Nazionale di Alta Matematica’ and of the ADAMSS Center of the Università degli Studi di Milano (Italy).

References

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