𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Local well-posedness and blow-up criteria of solutions for a rod equation

✍ Scribed by Yong Zhou

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
186 KB
Volume
278
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

In this paper we consider a new rod equation derived recently by Dai [Acta Mech. 127 No. 1–4, 193–207 (1998)] for a compressible hyperelastic material. We establish local well‐posedness for regular initial data and explore various sufficient conditions of the initial data which guarantee the blow‐up in finite time both for periodic and non‐periodic case. Moreover, the blow‐up time and blow‐up rate are given explicitly. Some interesting examples are given also. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

📜 SIMILAR VOLUMES

Blow-up profiles of solutions for the ex
Blow-up profiles of solutions for the exponential reaction-diffusion equation
✍ A. Pulkkinen 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 311 KB 👁 1 views

## Communicated by Marek Fila We consider the blow-up of solutions for a semilinear reaction-diffusion equation with exponential reaction term. It is known that certain solutions that can be continued beyond the blow-up time possess a non-constant self-similar blowup profile. Our aim is to find th

Blow-Up of Solutions with Sign Changes f
Blow-Up of Solutions with Sign Changes for a Semilinear Diffusion Equation
✍ Noriko Mizoguchi; Eiji Yanagida 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 117 KB

0 with the Dirichlet, Neumann, or periodic boundary condition. Here ) 0 is a Ž . parameter, and f is an odd function of u satisfying f Ј 0 ) 0 and some convexity Ž . w x condition. Let z U be the number of times of sign changes for U g C 0, 1 . It is Ä 4 shown that there exists an increasing sequenc

Global existence and blow-up of the solu
Global existence and blow-up of the solutions for the multidimensional generalized Boussinesq equation
✍ Ying Wang; Chunlai Mu 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 149 KB 👁 1 views

## Abstract In this paper, the existence and the uniqueness of the global solution for the Cauchy problem of the multidimensional generalized Boussinesq equation are obtained. Furthermore, the blow‐up of the solution for the Cauchy problem of the generalized Boussinesq equation is proved. Copyright

Uniform blow-up profile and boundary beh
Uniform blow-up profile and boundary behaviour for a non-local reaction–diffusion equation with critical damping
✍ Philippe Souplet 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 107 KB

## Abstract We consider the Dirichlet problem for a non‐local reaction–diffusion equation with integral source term and local damping involving power non‐linearities. It is known from previous work that for subcritical damping, the blow‐up is global and the blow‐up profile is uniform on all compact