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EnglishWe investigate existence, nonexistence and asymptotical behaviour-both at the origin and at infinity-of radial self-similar solutions to a semilinear parabolic equation with inverse-square potential. These solutions are relevant to prove nonuniqueness of the Cauchy problem for the parabolic equation in certain Lebesgue spaces, generalizing the result proved by Haraux and Weissler [Non-uniqueness for a semilinear initial value problem, Indiana Univ. Math. J. 31 (1982) 167-189] for the case of vanishing potential.
http://hdl.handle.net/11573/3086| Titolo: | Nonexistence of local solutions to semilinear partial differential inequalities |
| Autori interni: | TESEI, Alberto |
| Data di pubblicazione: | 2004 |
| Rivista: | ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE |
| Abstract: | We investigate existence, nonexistence and asymptotical behaviour-both at the origin and at infinity-of radial self-similar solutions to a semilinear parabolic equation with inverse-square potential. These solutions are relevant to prove nonuniqueness of the Cauchy problem for the parabolic equation in certain Lebesgue spaces, generalizing the result proved by Haraux and Weissler [Non-uniqueness for a semilinear initial value problem, Indiana Univ. Math. J. 31 (1982) 167-189] for the case of vanishing potential. |
| Handle: | http://hdl.handle.net/11573/3086 |
| Appare nelle tipologie: | 01.a Pubblicazione su Rivista |
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