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 -