Initial value problems in Clifford-type analysis

Original · EN

We consider an initial value problem of type ∂ u/∂ t= F(t,x,u,∂ⱼ u), u(0,x)=ϕ(x), where t is the time, x ∈ Rⁿ and u₀ is a Clifford type algebra-valued function satisfying Du=∑ⱼ₌₀ⁿλⱼ(x)eⱼ∂ⱼu = 0, λⱼ(x)∈ R for all j. We will solve this problem using the technique of associated spaces. In order to do that, we give sufficient conditions on the coefficients of the operators F and D, where F(u)= ∑ᵢ₌₀ⁿA⁽ⁱ⁾(x)∂ᵢu for A⁽ⁱ⁾(x) ∈ R or A⁽ⁱ⁾(x) belonging to a Clifford-type algebra, such that these operators are an associated pair.