Nonlinear heat equations in two dimensions with singular initial data are studied. In recent works nonlinearities with exponential growth of Trudinger-Moser type have been shown to manifest critical behavior: well-posedness in the subcritical case and non-existence for certain supercritical data. In this article we propose a specific model nonlinearity with Trudinger-Moser growth for which we obtain surprisingly complete results: a) for initial data strictly below a certain singular threshold function u˜ the problem is well-posed, b) for initial data above this threshold function u˜, there exists no solution, c) for the singular initial datum u˜ there is non-uniqueness. The function u˜ is a weak stationary singular solution of the problem, and we show that there exists also a regularizing classical solution with the same initial datum u˜.
Non-uniqueness for a critical heat equation in two dimensions with singular data / N. Ioku, B. Ruf, E. Terraneo. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - 36:7(2019 Nov), pp. 2027-2051.
Titolo: | Non-uniqueness for a critical heat equation in two dimensions with singular data |
Autori: | |
Parole Chiave: | Non-existence; Non-uniqueness; Nonlinear heat equation; Singular initial data |
Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica |
Data di pubblicazione: | nov-2019 |
Rivista: | |
Tipologia: | Article (author) |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.anihpc.2019.07.004 |
Appare nelle tipologie: | 01 - Articolo su periodico |