Asymptotic Analysis - Volume 36, issue 3-4

Authors: Nandakumaran, A.K. | Rajesh, M. | Mallikarjuna Rao, K.S.

Article Type: Research Article

Abstract: In this article we study the homogenization, of a particular example, of degenerate elliptic equations of second order in the setup of viscosity solutions. These results are an attempt to extend the corresponding results of Evans [8] to degenerate situations.

Citation: Asymptotic Analysis, vol. 36, no. 3-4, pp. 187-201, 2003

Authors: Vakulenko, S.A.

Article Type: Research Article

Abstract: The paper is devoted to localized reaction fronts in a viscous fluid. A rigorous analytical theory describing small front deformations is suggested, and the dependence of the front orientation on the gravity force is studied. Estimates for perturbation of the front velocity are given. The critical Rayleigh number when the convective instability appears is found.

Citation: Asymptotic Analysis, vol. 36, no. 3-4, pp. 203-239, 2003

Authors: Bidaut‐Véron, Marie‐Françoise | García‐Huidobro, Marta | Yarur, Cecilia

Article Type: Research Article

Abstract: We consider the semilinear parabolic system with absorption terms in a bounded domain Ω of $\mathbb{R}^{N}$ \[\left\{\begin{array}{l@{\quad}l}u_{t}-\Delta u+\vert v\vert ^{p}\vert u\vert ^{k-1}u=0,&\hbox{in }\varOmega\times(0,\infty),\\v_{t}-\Delta v+\vert u\vert ^{q}\vert v\vert ^{\ell -1}v=0,&\hbox{in }\varOmega\times(0,\infty),\\u(0)=u_{0},\quad v(0)=v_{0},&\hbox{in }\varOmega,\end{array}\right.\] where p,q>0 and k,ℓ≥0, with Dirichlet or Neuman conditions on $\curpartial\varOmega\times(0,\infty)$ . We study the existence and uniqueness of the Cauchy problem when the initial data are L1 functions or bounded measures. We find invariant regions when u0 , v0 are nonnegative, and give sufficient conditions for positivity or extinction in finite time.

Citation: Asymptotic Analysis, vol. 36, no. 3-4, pp. 241-283, 2003

Authors: Rocca, Elisabetta | Schimperna, Giulio

Article Type: Research Article

Abstract: A phase‐field model of Penrose–Fife type for diffusive phase transitions with conserved order parameter is introduced. A Cauchy–Neumann problem is considered for the related parabolic system which couples a nonlinear Volterra integro‐differential equation for the temperature $\teta$ with a fourth order relation describing the evolution of the phase variable χ. The latter equation contains a relaxation parameter μ related to the speed of the transition process, which happens to be very small in the applications. Existence and uniqueness for this model as μ>0 have been recently proved by the first author. Here, the asymptotic behaviour of the model …is studied as μ is let tend to zero. By a priori estimates and compactness arguments, the convergence of the solutions is shown. The approximating initial data have to be properly chosen. The problem obtained at the limit turns out to couple the original energy balance equation with an elliptic fourth order inclusion. Show more

Keywords: phase transition, Penrose–Fife model, singular limit, Neumann problem, memory kernel

Citation: Asymptotic Analysis, vol. 36, no. 3-4, pp. 285-301, 2003

Authors: Benkirane, A. | Elmahi, A. | Meskine, D.

Article Type: Research Article

Abstract: We prove an existence and uniqueness result for solutions of some bilateral problems with right‐hand side in L1 by using an approach involving increasing powers.

Keywords: strongly nonlinear elliptic problem in $L^{1}$, truncations, obstacle problem

Citation: Asymptotic Analysis, vol. 36, no. 3-4, pp. 303-317, 2003

Authors: Amar, Micol | Berrone, Lucio R. | Gianni, Roberto

Article Type: Research Article

Abstract: The framework of this paper is given by the mixed boundary‐value problem \[\left\{\begin{array}{@{}l@{\quad}l}\Delta u(x)=0,&x;\in \Omega,\\u(x)=0,&x;\in \Gamma _{0},\\\frac{\partial u}{\partial n}(x)=q(x),&x;\in \Gamma _{1},\end{array}\right.\] where Ω is a plane domain bounded by a regular curve composed by two arcs Γ0 and Γ1 . Assuming that |Γ1 |=ε and denoting by u[ε] the solution to this problem, we study some asymptotic expansions in terms of ε which are related to u[ε]. Some connections are presented among these expansions, on one hand, and the geometry of the domain Ω, on the other. In addition, a systematic way is found for computing …at the boundary the Ghizzetti's integral that solves the problem. Show more

Citation: Asymptotic Analysis, vol. 36, no. 3-4, pp. 319-343, 2003

Authors: Almog, Y.

Article Type: Research Article

Abstract: The creeping motion of a Newtonian fluid around a particle in a smooth domain is studied. It is proved that the force distribution on the surface of the particle can be approximated, in the limit where the ratio between particle size and the domain's radius of curvature tends to zero, by the force distribution on the same particle near a flat wall. This result is then utilized to show that the velocities of the particle in mobility problems, or the forces acting on it in resistance problems can be approximated by replacing the domain with a flat wall.

Citation: Asymptotic Analysis, vol. 36, no. 3-4, pp. 345-357, 2003

Article Type: Other

Citation: Asymptotic Analysis, vol. 36, no. 3-4, pp. 359-360, 2003