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In this paper, we investigate the exponential time decay rate of solutions toward traveling waves for the Cauchy problem of generalized Benjamin–Bona–Mahony–Burgers equations (E)ut−utxx−νuxx+βux+f(u)x=0,t>0,x∈R with prescribed initial data (I)u(0,x)=u0(x)→u±,asx→±∞. Here ν(>0), β∈R are constants, u± are two given constants satisfying u+≠u− and the nonlinear function f(u)∈C2(R) is assumed to...
In this paper we investigate the exponential time decay rate of solutions toward traveling waves for the Cauchy problem of generalized Korteweg–de Vries–Burgers equations (E)ut+δuxxx−νuxx+f(u)x=0,t>0,x∈R with prescribed initial data (I)u(x,0)=u0(x)→u±,asx→±∞. Here δ≠0 and ν>0 are real constants, u+≠u− are two given constants and the smooth nonlinear function f(u) is assumed to be either convex...
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