| Título: | Symmetrization techniques on unbounded domains: Application to a chemotaxis system on R-N |
| Autores: | Díaz Díaz, Jesús Ildefonso ; Nagai, Toshitaka ; Rakotoson, Jean Michel Theresien |
| Tipo de documento: | texto impreso |
| Editorial: | Elsevier, 1998-05-01 |
| Dimensiones: | application/pdf |
| Nota general: | info:eu-repo/semantics/restrictedAccess |
| Idiomas: | |
| Palabras clave: | Estado = Publicado , Materia = Ciencias: Matemáticas: Análisis funcional y teoría de operadores , Tipo = Artículo |
| Resumen: |
The authors study the parabolic-elliptic system on RN: ?u/?t=??(?u??u?v), 0=?v??v+?u, u(0,?)=u0, a version of the mathematical model of chemotaxis proposed by Keller and Segel. A differential inequality for the quantity ?s0u?(t,?)d?, where u? is the decreasing rearrangement of the solution u(t,?) with respect to the spatial variable, is obtained. As a consequence, they obtain e.g. Lp-bounds of the solution (u,v) on R2 and global-in-time existence of solutions under the condition ???R2u08?, then the solution (u,v) blows up in a finite time. Compared to the previous work of Díaz Díaz and Nagai [Adv. Math. Sci. Appl. 5 (1995), no. 2, 659--680; MR1361010 (96j:35246)], where this problem has been considered on bounded domains of RN, there are some additional technical difficulties connected with the regularity of the derivative ?u?/?t. |
| En línea: | https://eprints.ucm.es/id/eprint/15695/1/86.pdf |
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