TY - JOUR

T1 - A Note on the existence of traveling-wave solutions to a boussinesq system

AU - Oliveira, Filipe

N1 - The author was partially supported by FCT (Portuguese Foundation for Science and Technology) through the grant PEst-OE/MAT/UI0209/2011.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - We obtain a one-parameter family (uμ(x,t),ημ(x,t))μ≥μ0=(φμ(x-ωμt),ψμ(x-ωμt))μ≥μ0 of traveling-wave solutions to the Boussinesq system {ut+ηx+uux+cηxxx=0(x,t)∈R2ηt+ux+(ηu)x+auxxx=0, in the case a,c<0 with non-null speeds ωμ arbitrarily close to 0 (ωμ-→0-μ→+∞). We show that the L2-size of such traveling-waves satisfies the uniform (in μ) estimate φμ22+ψμ22≤C√|a|+|c|,μ2+ψμ2≤C|a|+|c|, where C is a positive constant. Furthermore, φμ and-ψμ are smooth, non-negative, radially decreasing functions which decay exponentially at infinity.

AB - We obtain a one-parameter family (uμ(x,t),ημ(x,t))μ≥μ0=(φμ(x-ωμt),ψμ(x-ωμt))μ≥μ0 of traveling-wave solutions to the Boussinesq system {ut+ηx+uux+cηxxx=0(x,t)∈R2ηt+ux+(ηu)x+auxxx=0, in the case a,c<0 with non-null speeds ωμ arbitrarily close to 0 (ωμ-→0-μ→+∞). We show that the L2-size of such traveling-waves satisfies the uniform (in μ) estimate φμ22+ψμ22≤C√|a|+|c|,μ2+ψμ2≤C|a|+|c|, where C is a positive constant. Furthermore, φμ and-ψμ are smooth, non-negative, radially decreasing functions which decay exponentially at infinity.

UR - http://www.scopus.com/inward/record.url?scp=85028696514&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85028696514

VL - 29

SP - 127

EP - 136

JO - Differential and Integral Equations

JF - Differential and Integral Equations

SN - 0893-4983

IS - 1-2

ER -