Global solution, Fujita critical exponent, Diffusion Equation, Heat Dissipation Equation

What is it about?

Based on a self-similar analysis of the Fujita type global solvability, we obtain estimates for a solution and fronts (a free boundary) of the Cauchy problem for a doubly nonlinear nondivergence-form parabolic equation with variable density. We consider the case where the absorpiton depends on time and study the asymptotic behavior of the finite self-similar solution depending on numerical parameters characterizing a nonlinear medium. The main results are illustrated by numerical examples.

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Photo by Benjamín Gremler on Unsplash

Photo by Benjamín Gremler on Unsplash

Why is it important?

The deep learning technology for image denoising has many scholars’ research, but neural network research, due to the barriers of hardware, has not been developed, making the neural network technology no longer have a complex network model of computation for too much worry because high-performance GPU multicore parallel computing is well suited for the neural network model and is a necessary prerequisite for the rise of deep learning. Although a lot of people are beginning to study abroad, after all, the direction is the forward direction, and theory and technology are not very mature. Although the use of the image denoising aspect has really achieved good results, there are still many problems, so continuing research, perfecting the image denoising theory, and improving the effect of denoising are very necessary. Based on the diffusion equation and deep learning (CNN) algorithm, this paper adopts multi-feature extraction technology to study the richer features of the input image in the deep network and designs an image denoising network model based on deep residual learning of a convolutional network that has better denoising performance.

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