Convection-diffusion equations with random initial conditions. (English) Zbl 1412.35371
Summary: We consider an evolution equation generalising the viscous Burgers equation supplemented by an initial condition which is a homogeneous random field. We develop a non-linear framework enabling us to show the existence and regularity of solutions as well as their long time behaviour.
MSC:
| 35R11 | Fractional partial differential equations |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
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