The Cauchy problem for quasilinear pseudodifferential equation with integral coefficients

Abstract

We consider a quasilinear pseudodifferential evolution equation with the derivative of order one with respect to the time variable t and the pseudodifferential operator this symbol ar (σ), σ € ℝ , homogeneous order 0 < y ≤ 2, by space variable x with integral coefficients. Such equations describe diffusion on inhomogeneous fractals.