Search academic texts

Information × Registration Number 0209U005089, 0106U000591 , R & D reports Title The numerical–asymptotic methods of solving the nonlinear singular indignant “filtration–convection–diffusion” type problems with aftereffect and managing. popup.stage_title Head Bomba Andriy Yaroslavovych, Registration Date 15-01-2009 Organization Rivne State Humanitarian University popup.description2 Research object is nonlinear singularly perturbed boundary–value problems for the parabolic and elliptic equations systems with managing parameters in simple and double– connected domains with free borders, which are mathematical models of ecological and power systems under the conditions of interference of process and environment characteristics. Work purpose is the essentially new approach development of extended precision numerical asymptotical solutions constructions of nonlinearly singularly perturbed boundary–value problems for the parabolic and elliptic type differential equations in the partial derivatives systems (mathematics convective diffusion and filtration processes in porous deformed environment models under the conditions of process and environment characteristics interference) in difficult configuration areas under conditions of optimization and management. The algorithm of numerical solving of model nonlinear boundary–value problems on quasiconformal mappings in the domains restricted by two equipotential lines and two flow lines is modificated for the cases, when one of the boundary regions is unknown (free) curve with the fixed ends and for the case of the domains with free boundaries, inclusions, aftereffect and management. System approach to solution of model boundary–value problems on the conformal mappings in the domains with indeterminate boundary regions is built. Integral characteristics of built problems solutions (such as a full filtration consumption; a size of overflow etc.) and corresponding “optimization” ratios are received. Asymptotic developments of solutions of the problems, which describe nonlinear processes of convective diffusion in simply connected areas, restricted by flow lines and equipotential lines are received. Asymptotic approximations of spatial nonlinear model problems solutions in condition of inverse influence (with late) of polluting substance concentration on diffusion coefficient are built. Asymptotic development of inverse singularly perturbed boundary value “convection–diffusion” type problems with unknown diffusion coefficient depending on the doubly–connected domain coordinates and on the time is built. The analysis of operation of Minc’s filters by variable determinate entering concentration is carried out. Product Description popup.authors popup.nrat_date 2020-04-02 Close