We consider a question posed in [1], namelytheblow-upofthePDEut+(b(t, x)u1+k)x=uxxwhenbisuniformlybounded,Lipschitzandk=2.WegiveacompleteanswertothebehaviorofsolutionswhenbbelongstotheLorentzspacesb is an element of Lp,infinity,p is an element of(2,infinity],orbx is an element of Lp,infinity,p is an element of(1,infinity].(c) 2024ElsevierInc.Allrightsarereserved,includingthosefortextanddatamining,AItraining,andsimilartechnologies.
