Évènement

Date(s) : 01/03/2016   iCal
11h00 - 12h00

$We\; consider\; a\; family\; of\; positive\; solutions\; to\; the\; system\; of\; k\; components\; \$-\backslash Delta\; u\_\{i,\backslash beta\}=f(x,u\_\{i,\backslash beta\})-\backslash beta\; u\_\{i,\backslash beta\}\backslash sum\_\{j\backslash neq\; i\}a\_\{i,j\}u\_\{j,\backslash beta\}^2\$\; in\; \$\backslash Omega\; \backslash subset\; R^N\$\; with\; \$N\backslash geq\; 2\$.\; It\; is\; known\; that\; uniform\; bounds\; in\; \$L^\{\backslash infty\}\$\; of\; \$\backslash lbrace\; u\_\{\backslash beta\}\backslash rbrace\$\; imply\; convergence\; of\; the\; densities\; to\; a\; segregated\; configuration,\; as\; the\; competition\; parameter\; \$\backslash beta\$\; diverges\; to\; \$+\backslash infty\$.\; In\; this\; talk\; I\; will\; discuss\; how\; to\; obtain\; sharp\; quantitative\; point-wise\; estimates\; for\; the\; densities\; around\; the\; interface\; between\; different\; components,\; and,\; more\; specifically,\; how\; to\; characterize\; the\; asymptotic\; profile\; of\; \$u\_\{\backslash beta\}\$\; in\; terms\; of\; entire\; solutions\; to\; the\; limit\; system\; \$-\backslash Delta\; U\_i\; =\; U\_i\backslash sum\_\{j\backslash neq\; i\}a\_\{ij\}U\_j^2\$.\; These\; results\; are\; part\; of\; an\; ongoing\; project\; with\; Nicola\; Soave.$

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