Semilinear p-evolution equations in Sobolev spaces

TL;DR

This paper establishes local well-posedness results for semi-linear p-evolution equations with complex coefficients in Sobolev spaces, under decay conditions on the imaginary parts of the coefficients.

Contribution

It provides new well-posedness results for p-evolution equations with complex coefficients, extending previous work to include decay conditions on the imaginary parts.

Findings

Proved local well-posedness in Sobolev spaces for the equations.

Established decay conditions on the imaginary parts of coefficients.

Extended the theory to include complex-valued lower order terms.

Abstract

We prove local in time well-posedness in Sobolev spaces of the Cauchy problem for semi-linear p-evolution equations of the first order with real principal part, but complex valued coefficients for the lower order terms, assuming decay conditions on the imaginary parts as |x| goes to infinity.