Dissipation mechanics and exact solutions for nonlinear equations of dissipative type. Principle and application of dissipation mechanics. I
type: Item
instance of: scholarly article
title: Dissipation mechanics and exact solutions for nonlinear equations of dissipative type. Principle and application of dissipation mechanics. I
zbMATH Open document ID: 0626.76004
DOI: 10.1007/BF01896976
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1986-01-01T00:00:00Z
review text: Basing on the complementarity principle we build up a dissipation mechanics theory. It is a dissipative theory of correspondence with quantum mechanics. From this theory we can jointly handle problems of macroscopic non-equilibrium thermodynamics and viscous hydrodynamics, and handle each dissipative and irreversible problem in quantum mechanics. We prove the basic equations of dissipation mechanics to eigenvalues equations of correspondence with the Schrödinger equation or Dirac equation. We merge the basic nonlinear equations of dissipative type, especially the Navier-Stokes equation as a basic equation for macroscopic non- equilibrium thermodynamics and viscous hydrodynamics into integrability condition of basic equation of dissipation mechanics. We obtain exact solutions by the inverse scattering method.
Mathematics Subject Classification ID: 76A02
Mathematics Subject Classification ID: 76R99
Mathematics Subject Classification ID: 82B10
Mathematics Subject Classification ID: 82B35
zbMATH DE Number: 4018585
zbMATH Keywords: dissipation mechanics
zbMATH Keywords: macroscopic non-equilibrium thermodynamics
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: Dirac equation
author: Hui-chuan Shen
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01896976
OpenAlex ID: W2001450330
description: scientific article; zbMATH DE number 4018585