Dispersion vs. anti-diffusion: Well-posedness in variable coefficient and quasilinear equations of KdV-type
Dispersion vs. anti-diffusion: Well-posedness in variable coefficient and quasilinear equations of KdV-type
We study the well-posedness of the initial value problem on periodic intervals for linear and quasilinear evolution equations for which the leading-order terms have three spatial derivatives.In such equations, there is a competition between the dispersive effects which stem from the leadingorder term, and anti-diffusion which stems from the lower-order …