Here we consider a class of non-linear heat equation with polynomial non-linearity. We prove a non-uniqueness result for mild solutions which take values in a critical Lebesgue space. To this end we extend to the entire space a counter-example of Ni and Sacks in the case where the underlying space is the ball of center 0 and of radius 1. We also propose a new criterion of uniqueness optimal with respect to the given counter-examples. The proof of our results lie on some estimates for the heat kernel in Lorentz spaces introduced by Meyer in the Navier-Stokes context.

Non-uniqueness for a critical non-linear heat equation / E. Terraneo. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - 27:1-2(2002), pp. 185-218. [10.1081/PDE-120002786]

Non-uniqueness for a critical non-linear heat equation

E. Terraneo
Primo
2002

Abstract

Here we consider a class of non-linear heat equation with polynomial non-linearity. We prove a non-uniqueness result for mild solutions which take values in a critical Lebesgue space. To this end we extend to the entire space a counter-example of Ni and Sacks in the case where the underlying space is the ball of center 0 and of radius 1. We also propose a new criterion of uniqueness optimal with respect to the given counter-examples. The proof of our results lie on some estimates for the heat kernel in Lorentz spaces introduced by Meyer in the Navier-Stokes context.
2002
http://www.informaworld.com/smpp/content?content=10.1081/PDE-120002786
Article (author)
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/27391
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 35
  • ???jsp.display-item.citation.isi??? 33
social impact