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.
Nonexistence of local solutions to semilinear partial differential inequalities / Pohozhaev, S. I.; Tesei, Alberto. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - STAMPA. - 21:(2004), pp. 487-502. [10.1016/j.anihpc.2003.06.002]
Nonexistence of local solutions to semilinear partial differential inequalities
TESEI, Alberto
2004
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
