The existence of the classical global solutions for the non-linear Klein-Gordon-Schro¨dinger equations is proved in H-subcritical cases for space dimensions n)5. For higher space dimensions 6)n)9, we will give a subsequent paper to deal with.
On global solutions for non-linear Hamiltonian evolution equations
✍ Scribed by J. Marsden
- Publisher
- Springer
- Year
- 1973
- Tongue
- English
- Weight
- 119 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0010-3616
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract In this paper, the global existence and uniqueness of smooth solution to the initial‐value problem for coupled non‐linear wave equations are studied using the method of a priori estimates.
The paper deals with global-in-time solutions of semi-linear evolution equations in circular domains. These solutions are constructed by means of the series of eigenfunctions of the Laplace operator in the corresponding region. A forced Cahn-Hilliardtype equation in a unit disc Ω is considered as an
## Abstract The Cauchy problem for semilinear wave equations u~tt~ − Δ__u__ + __h__(|__x__|)__u__^__p__^ = 0 with radially symmetric smooth ‘large’ data has a unique global classical solution in arbitrary space dimensions if __h__ is non‐negative and __p__ any odd integer provided the smooth factor