Opuscula Math. 38, no. 1 (2018), 41-80
https://doi.org/10.7494/OpMath.2018.38.1.41

Opuscula Mathematica

# Asymptotic profiles for a class of perturbed Burgers equations in one space dimension

F. Dkhil
M. A. Hamza
B. Mannoubi

Abstract. In this article we consider the Burgers equation with some class of perturbations in one space dimension. Using various energy functionals in appropriate weighted Sobolev spaces rewritten in the variables $$\frac{\xi}{\sqrt\tau}$$ and $$\log\tau$$, we prove that the large time behavior of solutions is given by the self-similar solutions of the associated Burgers equation.

Keywords: Burgers equation, self-similar variables, asymptotic behavior, self-similar solutions.

Mathematics Subject Classification: 35B20, 35B40, 35C20, 35K55, 35L05, 35L60.

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