Gevrey well posedness for $3$-evolution equations with variable coefficients

Abstract

We study the Cauchy problem for a class of third order linear anisotropic evolution equations with complex valued lower order terms depending both on time and space variables. Under suitable decay assumptions for $|x|\to \infty$ on these coefficients, we prove a well posedness result in Gevrey-type spaces.

29 pages

References in corpus (2)

• Semilinear p-evolution equations in Sobolev spaces
• Singularity for Solutions of Linearized KdV Equations