Contenu
Convergence de la solution de l’équation de Burgers visqueuse non homogène vers une solution stationnaire
Hisao Fujita YASHIMA 1), Nardjes TROUDI 2)
et Naima KHELOUFI3)
École Normale Supérieure de Constantine, Algérie
Mathematics Subject Classification: (MSC 2010) 35K59, 35B4; 42A75
Key words : Nonhomogeneous viscous Burgers equation, asymptotic
behavior, convergence to the stationary solution.
Abstract:
We consider the nonhomogeneous viscous Burgers equation ∂tu + u∂xu = ε∂x2u + ε2μsinx on ℝ and prove that there exists a number μ > 0 such that, if |μ| < μ, then the solution of this equation converges for t →∞ to the stationary solution u(x) = εw(x) with w(x) which does not depend on ε. To prove it, we transform the equation into a linear parabolic equation and prove the convergence of the solution of the latter equation for t →∞.