Affiliation:
1. Department of Mathematics , Chungnam National University , Daejeon 34134 , Republic of Korea
Abstract
Abstract
In this paper, we will study the behavior of the solutions of the linear parabolic equation with Dirichlet conditions when the domain is perturbed in the
C
1
{C^{1}}
topology. More precisely, it is shown that the solutions of this equation are stable under such perturbations.
Funder
National Research Foundation of Korea
Subject
Applied Mathematics,General Mathematics
Reference16 articles.
1. J. M. Arrieta,
Domain dependence of elliptic operators in divergence form,
Resenhas IME-USP 3 (1997), 107–122.
2. J. M. Arrieta and A. N. Carvalho,
Spectral convergence and nonlinear dynamics of reaction-diffusion equations under perturbations of the domain,
J. Differential Equations 199 (2004), no. 1, 143–178.
3. J. M. Arrieta, A. N. Carvalho and G. Lozada-Cruz,
Dynamics in dumbbell domains. I. Continuity of the set of equilibria,
J. Differential Equations 231 (2006), no. 2, 551–597.
4. I. Babuška and R. Výborný,
Continuous dependence of eigenvalues on the domain,
Czechoslovak Math. J. 15(90) (1965), 169–178.
5. R. Courant and D. Hilbert,
Methods of Mathematical Physics. Vol. I,
Interscience, New York, 1953.