𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the Cauchy Problem of Some Dissipative Flows

✍ Scribed by Dehua Wang

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
185 KB
Volume
218
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

The Cauchy problem is studied for a system of nonlinear partial differential equations for some dissipative flows in Lagrangian formulation including heat conduction, damping relaxation, and coupling to electric field. The well-posedness of smooth solutions is investigated. It is proved that, for certain large initial data, the solution will develop singularities and shock waves in finite time, which indicates that the Cauchy problem does not have global smooth solutions even if the initial data are smooth, and one has to seek weak solutions.

πŸ“œ SIMILAR VOLUMES

Some remarks on global existence to the
Some remarks on global existence to the Cauchy problem of the wave equation with nonlinear dissipation
✍ Nour-Eddine Amroun; AbbΓ¨s Benaissa πŸ“‚ Article πŸ“… 2008 πŸ› John Wiley and Sons 🌐 English βš– 160 KB πŸ‘ 1 views

## Abstract In this paper we prove the existence of global decaying __H__^2^ solutions to the Cauchy problem for a wave equation with a nonlinear dissipative term by constructing a stable set in __H__^1^(ℝ^__n__^ ). (Β© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

On the Cauchy problem for thermoelastic
On the Cauchy problem for thermoelastic plates
✍ Igor Chudinovich; Christian Constanda; JosΓ© ColΓ­n Venegas πŸ“‚ Article πŸ“… 2006 πŸ› John Wiley and Sons 🌐 English βš– 130 KB
Global Smooth Solutions to the Spatially
Global Smooth Solutions to the Spatially Periodic Cauchy Problem for Dissipative Nonlinear Evolution Equations
✍ Ling Hsiao; Huaiyu Jian πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 214 KB

The existence and uniqueness are proved for global classical solutions of the spatially periodic Cauchy problem to the following system of parabolic equations s y y ␣ y q ␣ Ž . which was proposed as a substitute for the Rayleigh᎐Benard equation and can lead to Lorenz equations.

The local Cauchy problem for multicompon
The local Cauchy problem for multicomponent reactive flows in full vibrational non-equilibrium
✍ Vincent Giovangigli; Marc Massot πŸ“‚ Article πŸ“… 1998 πŸ› John Wiley and Sons 🌐 English βš– 211 KB

## Communicated by J. C. Nedelec We consider reactive mixtures of dilute polyatomic gases in full vibrational non-equilibrium. The governing equations are derived from the kinetic theory and possesses an entropy. We recast this system of conservation laws into a symmetric conservative form by usin