Asymptotic expansion for the generalized Benjamin-Bona-Mahony-Burgers equation
This paper is devoted to the asymptotic expansion as \(t\to\infty\) of the solutions to the \(n\)-dimensional Benjamin-Bona-Makowy-Burgers equation: \[ \begin{cases} u_t-\Delta u_t-\Delta u+(b\cdot\nabla u)=\nabla\cdot F(u),\quad x\in\mathbb{R}^n,\;t>0\\ u(x,0)=u_0(x),\end{cases}\tag{1} \] where \(b\in\mathbb{R}^n\) and \(F\in C^1(\mathbb{R},\mathbb{R}^n)\) are a fixed vector and a vector field, respectively, and \(\nabla\) stands for the divergence operator. The authors compute also the second term in the asymptotic expansion with quadratic nonlinear term.
scientific article; zbMATH DE number 1839883