GUEMOULA AsmaMANSOUR AbdelouahabHECHIFA Abderazak2024-05-302024-05-302020-02-23GUEMOULA Asma, MANSOUR Abdelouahab, HECHIFA Abderazak. EXTENDED SPECTRUM, NUMERICAL RANGE OF OPERATORS AND ALUTHGE TRANSFORMATION AND INTERACTIONS. International PluridisciplinaryPhD Meeting (IPPM’20). 1st Edition, February23-26, 2020. University Of Eloued. [Visited in ../../….]. Available from [copy the link here].https://dspace.univ-eloued.dz/handle/123456789/32818InterventionThe aim of this paper is to show the existence, uniqueness, and asymptotic behavior of time-dependent solutions. Also in- vestigated is the existence of positive maximal and minimal so- lutions of the corresponding quasilinear elliptic system. The el- liptic operators in both systems are allowed to be degenerate in the sense that the density-dependent di¤usion coe¢ cients Di (ui) may have the property Di (0) = 0 for some or all i = 1;...;N, and the boundary condition is ui = 0. Using the method of up- per and lower solutions, we show that a unique global classical time-dependent solution exists and converges to the maximal so- lution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution.enquasilinear elliptic equationsdegenerate reac- tion di¤usion systemmethod of upper and lower solutionsIntervention