Geodesic
Comparison results for solutions of reaction diffusion problems
Glasgow mathematical journal, Tome 44 (2002) no. 3, pp. 483-495

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In this paper we construct upper bounds for the solutions u({\bf{x}},t) and its gradient |\nabla u| of a class of parabolic initial-boundary value problems in terms of the solution \psi ({\bf{x}}) of the {\text S}^t-Venant problem. These bounds are sharp in the sense that they coincide with the exact values of u and |\nabla u| for appropriate geometry and appropriate initial conditions. 
Philippin, Gérard A.; Piro, Stella Vernier. Comparison results for solutions of reaction diffusion problems. Glasgow mathematical journal, Tome 44 (2002) no. 3, pp. 483-495. doi: 10.1017/S0017089502030136
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     author = {Philippin, G\'erard A. and Piro, Stella Vernier},
     title = {Comparison results for solutions of reaction diffusion problems},
     journal = {Glasgow mathematical journal},
     pages = {483--495},
     year = {2002},
     volume = {44},
     number = {3},
     doi = {10.1017/S0017089502030136},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089502030136/}
}
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