Asymptotic Analysis - Volume 21, issue 3-4

Authors: Boni, Théodore K.

Article Type: Research Article

Abstract: We obtain some sufficient conditions under which solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions exist globally or blow up in a finite time. We also give the asymptotic behavior of solutions which tend to zero as t\rightarrow\infty . Finally, we obtain the asymptotic behavior near the blow‐up time of certain blow‐up solutions and describe their blow‐up set.

Keywords: Blow‐up, global existence, asymptotic behavior, maximum principle

Citation: Asymptotic Analysis, vol. 21, no. 3‐4, pp. 187-208, 1999

Authors: Demengel, Françoise

Article Type: Research Article

Citation: Asymptotic Analysis, vol. 21, no. 3‐4, pp. 209-220, 1999

Authors: Ramiandrisoa, Arthur

Article Type: Research Article

Abstract: Assuming that the maximal classical solution u of u_t-\Delta u=u^p on B(0,R) has, at time T_{\max} , a blow‐up set \mathbf{B}(u) that is not the singleton \left\{0\right\} , we prove that {\|u\|}_{L^q (\varOmega)} blows up for all q>(p-1)/2 , the energy blows up and u blows up completely after T_{\max} in the sense of Baras–Cohen (equivalent to the fact that there is no weak solution extending u beyond T_{\max} ). We also study this type of blow‐up through numerical experiments …as well as degenerate blow‐up. Show more

Keywords: Blow‐up, subcritical norms, radial solutions, heat equation, blow‐up set, numerical experiments

Citation: Asymptotic Analysis, vol. 21, no. 3‐4, pp. 221-238, 1999

Authors: Rodríguez, José M.

Article Type: Research Article

Abstract: In this paper we obtain a limit model for a turbine blade fixed to a 3D solid. This model is a three‐dimensional elasticity problem in the 3D part of the piece (the rotor) and a two‐dimensional problem (the shallow shell equations) in the 2D part (the turbine blade), with junction conditions in the part of the turbine blade fixed to the rotor. To obtain this model we shall do an asymptotic analysis, starting with the linear three‐dimensional elasticity equations on all the piece and taking as a small parameter the thickness of the blade. Finally, we shall make some comments …about what happens in the nonlinear case. Show more

Citation: Asymptotic Analysis, vol. 21, no. 3‐4, pp. 239-273, 1999

Authors: Paronetto, F.

Article Type: Research Article

Abstract: In this paper we study the homogenization problem of a sequence of degenerate linear parabolic operators \mu(h^{\gamma}x)\frac{\curpartial}{\curpartial t} - \mathrm{div}\big(a(h^{\gamma}x,h^{\beta}t) \cdot D \big) (\gamma, \beta \geq 0 ), where the matrix of the coefficients a(y,\tau) verifies the degenerate elliptic condition \lambda(y)\vert \xi\vert ^2\leq (a(y,\tau)\cdot \xi,\xi)\leq L\lambda(y) \vert \xi\vert ^2 , \lambda being a weight satisfying a Muckenhoupt’s condition (\lambda\in A_2 ) and (\mu,\lambda) being a pair of weights satisfying a generalized Muckenhoupt’s condition.

Citation: Asymptotic Analysis, vol. 21, no. 3‐4, pp. 275-302, 1999

Authors: Bourgeat, A. | Piatnitski, A.

Article Type: Research Article

Abstract: The work is giving estimations of the discrepancy between solutions of the initial and the homogenized problems for a one‐dimensional second‐order elliptic operators with random coefficients satisfying strong or uniform mixing conditions. We obtain several sharp estimates in terms of the corresponding mixing coefficient.

Keywords: Stochastic homogenization, random operators, moderate deviations

Citation: Asymptotic Analysis, vol. 21, no. 3‐4, pp. 303-315, 1999

Authors: Acerbi, Emilio | Braides, Andrea

Article Type: Research Article

Citation: Asymptotic Analysis, vol. 21, no. 3‐4, pp. 317-329, 1999

Authors: Jochmann, Frank

Article Type: Research Article

Abstract: In this paper the long time asymptotic behavior of solutions of Maxwell’s equations with electric conductivity in an exterior domain with mixed boundary conditions is investigated. It is shown that the solution behaves asymptotically like a free space solution provided it obeys a suitable local decay property. As a consequence, the completeness of the wave operators is obtained under very general assumptions on the coefficients.

Keywords: Maxwell’s equations, exterior boundary‐value problem, asymptotic behaviour, completeness of the wave operators

Citation: Asymptotic Analysis, vol. 21, no. 3‐4, pp. 331-363, 1999

Authors: The issue number is given in front of the page numbers.,

Article Type: Other

Citation: Asymptotic Analysis, vol. 21, no. 3‐4, pp. 365-366, 1999