Geodesic
GLOBAL EXISTENCE IN INFINITE LATTICES OF NONLINEAR OSCILLATORS: THE DISCRETE KLEIN-GORDON EQUATION
Glasgow mathematical journal, Tome 48 (2006) no. 3, pp. 463-482

Voir la notice de l'article provenant de la source Cambridge

DOI

Pointing out the difference between the Discrete Nonlinear Schrödinger equation with the classical power law nonlinearity – for which solutions exist globally, independently of the sign and the degree of the nonlinearity, the size of the initial data and the dimension of the lattice – we prove either global existence or nonexistence, in time, for the Discrete Klein-Gordon equation with the same type of nonlinearity (but of “blow-up” sign), under suitable conditions on the initial data, and sometimes on the dimension of the lattice. The results consider both the conservative and the linearly damped lattice. Similarities and differences with the continuous counterparts are remarked. We also make a short comment on the existence of excitation thresholds, for forced solutions of damped and parametrically driven Klein-Gordon lattices.
DOI : 10.1017/S001708950600317X
Mots-clés : 37L60, 37L15, 35Q55, 34C11 
KARACHALIOS, NIKOS I. GLOBAL EXISTENCE IN INFINITE LATTICES OF NONLINEAR OSCILLATORS: THE DISCRETE KLEIN-GORDON EQUATION. Glasgow mathematical journal, Tome 48 (2006) no. 3, pp. 463-482. doi: 10.1017/S001708950600317X
@article{10_1017_S001708950600317X,
     author = {KARACHALIOS, NIKOS I.},
     title = {GLOBAL {EXISTENCE} {IN} {INFINITE} {LATTICES} {OF} {NONLINEAR} {OSCILLATORS:} {THE} {DISCRETE} {KLEIN-GORDON} {EQUATION}},
     journal = {Glasgow mathematical journal},
     pages = {463--482},
     year = {2006},
     volume = {48},
     number = {3},
     doi = {10.1017/S001708950600317X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708950600317X/}
}
TY  - JOUR
AU  - KARACHALIOS, NIKOS I.
TI  - GLOBAL EXISTENCE IN INFINITE LATTICES OF NONLINEAR OSCILLATORS: THE DISCRETE KLEIN-GORDON EQUATION
JO  - Glasgow mathematical journal
PY  - 2006
SP  - 463
EP  - 482
VL  - 48
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S001708950600317X/
DO  - 10.1017/S001708950600317X
ID  - 10_1017_S001708950600317X
ER  - 
%0 Journal Article
%A KARACHALIOS, NIKOS I.
%T GLOBAL EXISTENCE IN INFINITE LATTICES OF NONLINEAR OSCILLATORS: THE DISCRETE KLEIN-GORDON EQUATION
%J Glasgow mathematical journal
%D 2006
%P 463-482
%V 48
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S001708950600317X/
%R 10.1017/S001708950600317X
%F 10_1017_S001708950600317X

Cité par Sources :