Journal ArticleDOI
Asymptotic behaviour of solutions of semilinear parabolic equations
Yu. V. Egorov,V. A. Kondratiev +1 more
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In this article, the asymptotic behavior of solutions of a second-order semilinear parabolic equation is analyzed in a cylindrical domain that is bounded in the space variables.Abstract:
The asymptotic behaviour of solutions of a second-order semilinear parabolic equation is analyzed in a cylindrical domain that is bounded in the space variables. The dominant term of the asymptotic expansion of the solution as is found. It is shown that the solution of this problem is asymptotically equivalent to the solution of a certain non-linear ordinary differential equation. Bibliography: 8 titles.read more
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The asymptotics of solutions to elliptic equations with nonlinear boundary conditions
TL;DR: Asymptotics of solutions to elliptic equations with nonlinear boundary conditions are studied in this paper, where the boundary condition is defined as a nonlinear mixture of the boundary conditions.
References
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Inverse Problem for a Curved Quantum Guide
Laure Cardoulis,Michel Cristofol +1 more
TL;DR: In this article, the Dirichlet Laplacian operator −∆ on a curved quantum guide in R n (n = 2, 3) with an asymptotically straight reference curve was considered, and uniqueness results for the inverse problem associated to the reconstruction of the curvature by using either observations of spectral data or a boot-strapping method were given.
Book
Équations elliptiques du second ordre à coefficients discontinus
TL;DR: In this paper, the conditions générales d'utilisation (http://www.numdam.org/legal.php) of a fichier do not necessarily imply a mention of copyright.
Journal ArticleDOI
Problèmes aux limites non homogènes (VI)
Journal ArticleDOI
Asymptotic behaviour of solutions of some nonlinear parabolic or elliptic equations
V.A. Kondratiev,Laurent Veron +1 more
TL;DR: In this paper, the authors studied the asymptotic behavior of the solutions of the parabolic equation (1) ∂u/∂t−Lu+a(x)|u|q−1u = 0 in Ω × (0,∞) when Ω is bounded, u satisfies the Neumann boundary condition in ∂Ω × ∞, L is a linear strongly elliptic operator in ∆, q is bigger than 1 and a(x)>0.