Abstract
In this paper a rigorous study concerning global existence results and estimates for the sup norm of non-negative bounded solutions for one-dimensional advection-diffusion equations ut+(b(x,t)uk+1)x=μ(t)uxx, with 0≤k<2 and initial data u0∈L1(R)∩L∞(R) is provided using a technique based on energy methods. In respect of the arbitrary advective speed term, it is only assumed that b(x,t) and ∂b(x,t)/∂x are limited.
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