Displaying similar documents to “Global existence and large time asymptotic bounds of L ∞ solutions of thermal diffusive combustion systems on ℝ n ”

Asymptotics for multifractal conservation laws

Piotr Biler, Grzegorz Karch, Wojbor Woyczynski (1999)

Studia Mathematica

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We study asymptotic behavior of solutions to multifractal Burgers-type equation u t + f ( u ) x = A u , where the operator A is a linear combination of fractional powers of the second derivative - ∂ 2 / ∂ x 2 and f is a polynomial nonlinearity. Such equations appear in continuum mechanics as models with fractal diffusion. The results include decay rates of the L p -norms, 1 ≤ p ≤ ∞, of solutions as time tends to infinity, as well as determination of two successive terms of the asymptotic expansion of solutions. ...

Improved estimates for the Ginzburg-Landau equation : the elliptic case

Fabrice Bethuel, Giandomenico Orlandi, Didier Smets (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We derive estimates for various quantities which are of interest in the analysis of the Ginzburg-Landau equation, and which we bound in terms of the G L -energy E ε and the parameter ε . These estimates are local in nature, and in particular independent of any boundary condition. Most of them improve and extend earlier results on the subject.