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).
The existence of global in space variables solution for non-linear subelliptic equation of floating water
β Scribed by Leszek Sidz
- Publisher
- John Wiley and Sons
- Year
- 1994
- Tongue
- English
- Weight
- 508 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0170-4214
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β¦ Synopsis
Abstract
The existence of global in space variables solutions for a class of nonβlinear subelliptic evolution operators is proved. A Cauchy problem and an initialβboundary value problem are considered using the contraction theorem and Galerkin methods.
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This paper studies the existence and the non-existence of global solutions to the initial boundary value problems for the non-linear wave equation The paper proves that every above-mentioned problem has a unique global solution under rather mild con"ning conditions, and arrives at some su$cient con
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