  The mixed scalar curvature of a foliated Riemannian manifold, i.e., an
averaged mixed sectional curvature, has been considered by several geometers.
We explore the Yamabe type problem: to prescribe the constant mixed scalar
curvature for a foliation by a conformal change of the metric in normal
directions only. For a harmonic foliation, we derive the leafwise elliptic
equation and explore the corresponding nonlinear heat type equation. We assume
that the leaves are compact submanifolds and the manifold is fibered instead of
being foliated, and use spectral parameters of certain Schr\"odinger operator
to find solution, which is attractor of the equation.
