Asymptotic Analysis - Volume 66, issue 1

Authors: Rault, Jean-François

Article Type: Research Article

Abstract: The Fujita phenomenon for nonlinear parabolic problems ∂t u=Δu+up in an exterior domain of RN under dissipative dynamical boundary conditions σ ∂t u+∂ν u=0 is investigated in the superlinear case. As in the case of Dirichlet boundary conditions (see Trans. Amer. Math. Soc. 316 (1989), 595–622 and Israel J. Math. 98 (1997), 141–156), it turns out that there exists a critical exponent p=1+2/N such that blow-up of positive solutions always occurs for subcritical exponents, whereas in the supercritical case global existence can occur for small non-negative initial data.

Keywords: nonlinear parabolic problems, dynamical boundary conditions, global solutions

DOI: 10.3233/ASY-2009-0954

Citation: Asymptotic Analysis, vol. 66, no. 1, pp. 1-8, 2010

Authors: Han-Kwan, Daniel

Article Type: Research Article

Abstract: Following Frénod and Sonnendrücker [SIAM J. Math. Anal. 32(6) (2001) 1227–1247], we consider the finite Larmor radius regime for a plasma submitted to a large magnetic field and take into account both the quasineutrality and the local thermodynamic equilibrium of the electrons. We then rigorously establish the asymptotic gyrokinetic limit of the rescaled and modified Vlasov–Poisson system in a three-dimensional setting with the help of an averaging lemma.

Keywords: gyrokinetic approximation, Vlasov–Poisson equation, finite Larmor radius scaling, averaging lemma

DOI: 10.3233/ASY-2009-0955

Citation: Asymptotic Analysis, vol. 66, no. 1, pp. 9-33, 2010

Authors: Samet, Bessem

Article Type: Research Article

Abstract: The topological sensitivity analysis consists to study the variation of a shape functional with respect to emerging of small holes in the interior of the domain occupied by the body. In this paper, we consider the case of a hole located at the boundary of the domain. The topological asymptotic expansion is derived for the Laplace equation in three cases: Dirichlet condition, Neumann condition and Robin condition on the boundary of the hole.

Keywords: topological derivative, Laplace equation, singularity

DOI: 10.3233/ASY-2009-0957

Citation: Asymptotic Analysis, vol. 66, no. 1, pp. 35-49, 2010

Authors: Rocha, E.M. | Rodrigues, M.M.

Article Type: Research Article

Abstract: A class of perturbed reaction–diffusion–convection (R–D–C) equations with reaction, diffusion and convection functions in nonuniform media is studied. By using singular perturbation analysis and Hamilton–Jacobi theory, the wavefront speed of such R–D–C equations is computed for different classes of nonlinearities.

Keywords: reaction–diffusion–convection, wavefront speed, singular perturbation analysis, Hamilton–Jacobi dynamics

DOI: 10.3233/ASY-2009-0958

Citation: Asymptotic Analysis, vol. 66, no. 1, pp. 51-59, 2010