We consider the well-posedness of the Cauchy problem for convection-diffusion equations in uniformly local Lebesgue spaces Lruloc(ℝn). In our setting, an initial function that is spatially periodic or converges to a nonzero constant at infinity is admitted. Our result is applicable to the one dimensional viscous Burgers equation. For the proof, we use the Lpuloc −Lquloc estimate for the heat semigroup obtained by Maekawa-Terasawa , the Banach fixed point theorem, and the comparison principle.
|Number of pages
|Differential and Integral Equations
|Published - 2021