The Blow-Up Rate for a Strongly Coupled System of Semilinear Heat Equations with Nonlinear Boundary Conditions

The paper deals with the blow-up rate of positive solutions to the system ut uxx ul11 l12, t xx ul21 l22 with boundary conditions uxŽ1, t. Žu p11 p12.Ž1, t. and xŽ1, t. Žu p21 p22 .Ž1, t.. Under some assumptions on the matrices L Žli j. and P Žpi j. and on the initial data u0, 0, the solution Žu, . blows up at finite time T, and we prove that max x 0, 1 uŽx, t. Žresp. max x 0, 1 Žx, t..goes to infinity asŽT t. 1 2Žresp.ŽT t. 2 2 ., where i 0 are the solutions ofŽP Id.Ž 1, 2.t Ž 1, 1.t.