Resolution of partial differential equations by rotation

摘要

In this paper we study the rotation in R3 and we apply it to resolve some partial differential equations and the system of partial differential equations. For this, define first the rotation R(ψ,θ,φ) matrix and it's inverse and we prove that they are an orthogonal matrix. Then we calculate the eigenvalues of R(ψ,θ,φ) for different cases. Finally, for particular values of ψ,θ and φ, we apply the rotation to eliminate some partial derivatives in partial differential and system of partial differential equations to resolve them.