Geodesic
An explicit Lyapunov function for reflection symmetric parabolic partial differential equations on the circle
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 69 (2014) no. 3, pp. 419-433

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An explicit Lyapunov function is constructed for scalar parabolic reaction-advection-diffusion equations under periodic boundary conditions. The non-linearity is assumed to be even with respect to the advection term. The method followed was originally suggested by H. Matano for, and limited to, separated boundary conditions. Bibliography: 20 titles.
Keywords: partial differential equations, variational methods, energy functional, periodic boundary conditions.
Mots-clés : convection, advection, reaction-diffusion equations 
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     author = {B. Fiedler and C. Grotta-Ragazzo and C. Rocha},
     title = {An explicit {Lyapunov} function for reflection symmetric parabolic partial differential equations on the circle},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {419--433},
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     number = {3},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2014_69_3_a1/}
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B. Fiedler; C. Grotta-Ragazzo; C. Rocha. An explicit Lyapunov function for reflection symmetric parabolic partial differential equations on the circle. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 69 (2014) no. 3, pp. 419-433. http://geodesic.mathdoc.fr/item/RM_2014_69_3_a1/