TY - JOUR
T1 - Long-time behavior of small solutions to quasilinear dissipative hyperbolic equations
AU - Milani, Albert
AU - Volkmer, Hans
PY - 2011/10/1
Y1 - 2011/10/1
N2 - We give sufficient conditions for the existence of global small solutions to the quasilinear dissipative hyperbolic equation u t t+2u t-a ij(u tu) α iα ju=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,v)α iα jv = h.We then give conditions for the convergence, as t-∞, of the solution of the evolution equation to its stationary state.
AB - We give sufficient conditions for the existence of global small solutions to the quasilinear dissipative hyperbolic equation u t t+2u t-a ij(u tu) α iα ju=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,v)α iα jv = h.We then give conditions for the convergence, as t-∞, of the solution of the evolution equation to its stationary state.
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U2 - 10.1007/s10492-011-0025-0
DO - 10.1007/s10492-011-0025-0
M3 - Article
AN - SCOPUS:84855442145
SN - 0862-7940
VL - 56
SP - 425
EP - 457
JO - Applications of Mathematics
JF - Applications of Mathematics
IS - 5
ER -