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

Fathi Dkhil | Zendy; Mohamed Ali Hamza | Zendy; Bechir Mannoubi | Zendy

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

Author(s) -

Fathi Dkhil,

Mohamed Ali Hamza,

Bechir Mannoubi

Publication year - 2017

Publication title -

opuscula mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.481

H-Index - 16

eISSN - 2300-6919

pISSN - 1232-9274

DOI - 10.7494/opmath.2018.38.1.41

Subject(s) - mathematics , class (philosophy) , dimension (graph theory) , space (punctuation) , mathematical analysis , pure mathematics , burgers' equation , partial differential equation , linguistics , philosophy , artificial intelligence , computer science

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

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