TY  - JOUR
ID  - Dkhil2018
LB  - Dkhil2018
AU  - Dkhil, F.
AU  - Hamza, M. A.
AU  - Mannoubi, B.
TI  - Asymptotic profiles for a class of perturbed Burgers equations in one space dimension
ST  - Asymptotic profiles for a class of perturbed Burgers equations in one space dimension
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2018
VL  - 38
IS  - 1
SP  - 41
EP  - 80
DO  - https://doi.org/10.7494/OpMath.2018.38.1.41
UR  - https://doi.org/10.7494/OpMath.2018.38.1.41
AB  - 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.
KW  - Burgers equation
KW  - self-similar variables
KW  - asymptotic behavior
KW  - self-similar solutions
SN  - 1232-9274
ER  -