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We study solutions for the one-dimensional problem of the Green-Lindsay and the Lord-Shulman theories with two temperatures. First, existence and uniqueness of weakly regular solutions are obtained. Second, we prove the exponential stability in the Green-Lindsay model, but the non-exponential stability for the Lord-Shulman model.

Let a be the topological graph shaped like the letter o. We denote by 0 the unique branching point of a , and by O and I the closures of the components of a \ {0} homeomorphics to the circle and the interval, respectively. A continuous map from a into itself satisfying that / has a fixed point in O, or / has a fixed point and /(0) € I is called a a map.… (More)

- M. C. Leseduarte, Ramón Quintanilla
- Asymptotic Analysis
- 2015

In this paper we investigate the asymptotic spatial behavior of the solutions for several models for the nerve fibers. First, our analysis deals with the coupling of two parabolic equations. We prove that, under suitable assumptions on the coefficients and the nonlinear function, the decay is similar to the one corresponding to the heat equation. A limit… (More)

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