Generalized solutions of nonlinear diffusion equations
type: Item
instance of: scholarly article
title: Generalized solutions of nonlinear diffusion equations
zbMATH Open document ID: 1009.35041
author: Hideo Deguchi
published in: Hiroshima Mathematical Journal
publication date: 2003-04-27T00:00:00Z
review text: The author found the generalization solution of the following Cauchy problem in the sense of Colombeau: \[ \begin{cases}\widetilde u_t+ f(x,t,\widetilde u)\widetilde u_x+ g(x, t,\widetilde u)\widetilde u= \widetilde\mu\widetilde u_{xx},\quad & x\in\mathbb{R},\;t> 0,\\ \widetilde u|_{t=0}= \widetilde u_0,\quad & x\in\mathbb{R},\end{cases} \] where \(\widetilde\mu\) is generalized constant. He proved the existence and uniqueness theorem and he showed the relationship between generalized solutions and classical solutions by using the pseudo-norm.
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 46F30
zbMATH DE Number: 1790846
zbMATH Keywords: Cauchy problem in the sense of Colombeau
reviewed by: Dohan Kim
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1151007645
OpenAlex ID: W2159819992
DOI: 10.32917/HMJ/1151007645
description: scientific article; zbMATH DE number 1790846