Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8899023 | Journal of Differential Equations | 2018 | 25 Pages |
Abstract
We deal with a stationary problem of a reaction-diffusion system with a conservation law under the Neumann boundary condition. It is shown that the stationary problem turns to be the Euler-Lagrange equation of an energy functional with a mass constraint. When the domain is the finite interval (0,1), we investigate the asymptotic profile of a strictly monotone minimizer of the energy as d, the ratio of the diffusion coefficient of the system, tends to zero. In view of a logarithmic function in the leading term of the potential, we get to a scaling parameter κ satisfying the relation ε:=d=logâ¡Îº/κ2. The main result shows that a sequence of minimizers converges to a Dirac mass multiplied by the total mass and that by a scaling with κ the asymptotic profile exhibits a parabola in the nonvanishing region. We also prove the existence of an unstable monotone solution when the mass is small.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Jann-Long Chern, Yoshihisa Morita, Tien-Tsan Shieh,