Logarithmic diffusion in 2D and intermediate 1D range
Logarithmic diffusion in 2D and intermediate 1D range
This chapter studies two transition situations where non-uniqueness plays an important role. The first deals with the range -1 < m ≤ 0 in n = 1, which looks like supercritical but contains the non-uniqueness phenomenon for the Cauchy problem. The second is the study of logarithmic diffusion in the plane, i.e., the case m = 0 for n = 2 which has many appealing features for the analyst and the geometer.
Keywords: intermediate range, logarithmic diffusion, weak smoothing effect, asymptotic behaviour, weak local effect
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