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In this paper we introduce and study a new feature-preserving nonlinear nonlocal diffusion equation for denoising signals. The proposed 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. We provide a mathematical analysis of the existence of the solution in the two dimensional case, but easily extensible to the one-dimensional model. Finally, we show some numerical experiments, which demonstrate the effectiveness of the new approach. [ABSTRACT FROM AUTHOR]

We present non-existence results for a system of non-linear parabolic equations with non-local diffusions posed either in $\mathbb{R}^{N} $ or in a bounded domain. Our method of proof is based on the test function method with a judicious choice of the test function. [ABSTRACT FROM AUTHOR]