Algebrization of Nonautonomous Differential Equations

[摘要] Given a planar system of nonautonomous ordinary differential equations,dw/dt=F(t,w), conditions are given for the existence of an associative commutative unital algebraAwith uniteand a functionH:Ω⊂R2×R2→R2on an open setΩsuch thatF(t,w)=H(te,w)and the mapsH1(τ)=H(τ,ξ)andH2(ξ)=H(τ,ξ)are Lorch differentiable with respect toAfor all(τ,ξ)∈Ω, whereτandξrepresent variables inA. Under these conditions the solutionsξ(τ)of the differential equationdξ/dτ=H(τ,ξ)overAdefine solutions(x(t),y(t))=ξ(te)of the planar system.

[学科分类] 应用数学