Abstract
We show that the nonlinear contraction semigroup generated by the Benjamin–Bona–Mahony equation with dissipative memory $$u_{t} - u_{txx} + u_{x} - \int_{0}^{\infty} g(s) u_{xx}(t-s)\, {\rm d}s + u^{p} u_{x} = 0$$ is exponentially stable for every $${p\in\mathbb{N}}$$ .
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