𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On a Global Solution and Asymptotic Behaviour for the Generalized Damped Extensible Beam Equation

✍ Scribed by Solange Kouémou Patcheu

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
346 KB
Volume
135
Category
Article
ISSN
0022-0396

No coin nor oath required. For personal study only.

✦ Synopsis

We prove the existence and uniqueness of global solutions for the Cauchy problem concerning the evolution equation

suggested by the study of plates and beams, where A is a linear operator in a Hilbert space H and M and g are real functions. We also study the asymptotic behaviour of the solutions, under suitable growth assumptions on the nonlinear term g.

📜 SIMILAR VOLUMES

Global existence, asymptotic behaviour,
Global existence, asymptotic behaviour, and global non-existence of solutions for damped non-linear wave equations of Kirchhoff type in the whole space
✍ Kosuke Ono 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 178 KB 👁 2 views

We study the global existence, asymptotic behaviour, and global non-existence (blow-up) of solutions for the damped non-linear wave equation of Kirchho! type in the whole space: , and '0, with initial data u(x, 0)"u (x) and u R (x, 0)"u (x).

Existence and asymptotic behaviour of so
Existence and asymptotic behaviour of solutions for a class of quasi-linear evolution equations with non-linear damping and source terms
✍ Yang Zhijian 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 170 KB 👁 1 views

## Abstract We consider a class of quasi‐linear evolution equations with non‐linear damping and source terms arising from the models of non‐linear viscoelasticity. By a Galerkin approximation scheme combined with the potential well method we prove that when __m__<__p__, where __m__(⩾0) and __p__ ar

Existence and nonexistence of global sol
Existence and nonexistence of global solutions to the Cauchy problem for a nonlinear beam equation
✍ Changming Song; Zhijian Yang 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 207 KB 👁 1 views

The paper studies the existence and nonexistence of global solutions to the Cauchy problem for a nonlinear beam equation arising in the model in variational form for the neo-Hookean elastomer rod where k 1 ,k 2 > 0 are real numbers, g(s) is a given nonlinear function. When g(s) = s n (where n 2 is