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.
Existence and blow-up for non-autonomous scalar conservation laws with viscosity / Bianchini, Stefano; Leccese, Giacomo Maria. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 542:1(2025). [10.1016/j.jmaa.2024.128761]
Existence and blow-up for non-autonomous scalar conservation laws with viscosity
Bianchini, Stefano;Leccese, Giacomo Maria
2025-01-01
Abstract
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.| File | Dimensione | Formato | |
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