Geodesic
Long-time behavior of small solutions to quasilinear dissipative hyperbolic equations
Applications of Mathematics, Tome 56 (2011) no. 5, pp. 425-457.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We give sufficient conditions for the existence of global small solutions to the quasilinear dissipative hyperbolic equation $$ u_{tt} + 2 u_t - a_{ij}(u_t,\nabla u)\partial _i\partial _j u = f $$ corresponding to initial values and source terms of sufficiently small size, as well as of small solutions to the corresponding stationary version, i.e. the quasilinear elliptic equation $$ -a_{ij}(0,\nabla v)\partial _i\partial _j v=h. $$ We then give conditions for the convergence, as $t\to \infty $, of the solution of the evolution equation to its stationary state.
DOI : 10.1007/s10492-011-0025-0
Classification : 35A01, 35B35, 35B40, 35J15, 35J60, 35L15, 35L70
Keywords: quasilinear evolution equation; quasilinear elliptic equation; a priori estimates; global existence; asymptotic behavior; stationary solutions 
@article{10_1007_s10492_011_0025_0,
     author = {Milani, Albert and Volkmer, Hans},
     title = {Long-time behavior of small solutions to quasilinear dissipative hyperbolic equations},
     journal = {Applications of Mathematics},
     pages = {425--457},
     publisher = {mathdoc},
     volume = {56},
     number = {5},
     year = {2011},
     doi = {10.1007/s10492-011-0025-0},
     mrnumber = {2852065},
     zbl = {1249.35072},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-011-0025-0/}
}
TY  - JOUR
AU  - Milani, Albert
AU  - Volkmer, Hans
TI  - Long-time behavior of small solutions to quasilinear dissipative hyperbolic equations
JO  - Applications of Mathematics
PY  - 2011
SP  - 425
EP  - 457
VL  - 56
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10492-011-0025-0/
DO  - 10.1007/s10492-011-0025-0
LA  - en
ID  - 10_1007_s10492_011_0025_0
ER  - 
%0 Journal Article
%A Milani, Albert
%A Volkmer, Hans
%T Long-time behavior of small solutions to quasilinear dissipative hyperbolic equations
%J Applications of Mathematics
%D 2011
%P 425-457
%V 56
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10492-011-0025-0/
%R 10.1007/s10492-011-0025-0
%G en
%F 10_1007_s10492_011_0025_0
Milani, Albert; Volkmer, Hans. Long-time behavior of small solutions to quasilinear dissipative hyperbolic equations. Applications of Mathematics, Tome 56 (2011) no. 5, pp. 425-457. doi : 10.1007/s10492-011-0025-0. http://geodesic.mathdoc.fr/articles/10.1007/s10492-011-0025-0/

Cité par Sources :