Classical change point analysis aims at (1) detecting abrupt changes in the mean of a possibly nonstationary time series and (2) identifying regions where exhibits piecewise constant behavior. In many applications however, it is more reasonable to assume that gradually smooth way. Those gradual may either be nonrelevant (i.e., small), or relevant for specific problem hand, present paper present...

We study the Cauchy problem for Euler-Poisson-Darboux equation, with a power nonlinearity:utt−uxx+μtut=tα|u|p,t>t0,x∈R, where μ>0, p>1 and α>−2. Here either t0=0 (singular problem) or t0>0 (regular problem). show that this model may be interpreted as semilinear wave equation borderline dissipation: existence of global small data solutions depends not only on p, but also parameter μ. Global weak...