TY - JOUR
T1 - On the critical nonlinear damped wave equation with large initial data
AU - Hayashi, Nakao
AU - Kaikina, Elena I.
AU - Naumkin, Pavel I.
N1 - Funding Information:
We thank the referee for useful comments and suggestions. The work of P.I.N. and E.I.K. is partially supported by CONACYT.
PY - 2007/10/15
Y1 - 2007/10/15
N2 - We study the nonlinear damped wave equation(0.1){(ut t + ut - Δ u = - | u |σ u, x ∈ Rn, t > 0,; u (0, x) = u0 (x), ut (0, x) = u1 (x), x ∈ Rn,) in the critical case of σ = frac(2, n). Our aim is to prove the large time asymptotic formulas for solutions of the Cauchy problem (0.1) without any restriction on the size of the initial data and on the spatial dimension.
AB - We study the nonlinear damped wave equation(0.1){(ut t + ut - Δ u = - | u |σ u, x ∈ Rn, t > 0,; u (0, x) = u0 (x), ut (0, x) = u1 (x), x ∈ Rn,) in the critical case of σ = frac(2, n). Our aim is to prove the large time asymptotic formulas for solutions of the Cauchy problem (0.1) without any restriction on the size of the initial data and on the spatial dimension.
KW - Asymptotic formulas
KW - Critical nonlinearity
KW - Dissipative wave equations
KW - Large data
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U2 - 10.1016/j.jmaa.2007.01.021
DO - 10.1016/j.jmaa.2007.01.021
M3 - Article
AN - SCOPUS:34250684852
SN - 0022-247X
VL - 334
SP - 1400
EP - 1425
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -