Consider the nonlinear heat equation(Formula presented.)in the unit ball of (Formula presented.), with Dirichlet boundary condition. Let (Formula presented.) be a radially symmetric, sign-changing stationary solution having a fixed number (Formula presented.) of nodal regions. We prove that the solution of (NLH) with initial value (Formula presented.) blows up in finite time if {pipe}λ -1{pipe} > 0 is sufficiently small and if p is sufficiently large. The proof is based on the analysis of the asymptotic behavior of (Formula presented.) and of the linearized operator (Formula presented.). © 2014 Springer Basel.
Sign-changing stationary solutions and blowup for a nonlinear heat equation in dimension two / Flavio, Dickstein; Pacella, Filomena; Berardino, Sciunzi. - In: JOURNAL OF EVOLUTION EQUATIONS. - ISSN 1424-3199. - STAMPA. - 14:3(2014), pp. 617-633. [10.1007/s00028-014-0230-x]
Sign-changing stationary solutions and blowup for a nonlinear heat equation in dimension two
PACELLA, Filomena;
2014
Abstract
Consider the nonlinear heat equation(Formula presented.)in the unit ball of (Formula presented.), with Dirichlet boundary condition. Let (Formula presented.) be a radially symmetric, sign-changing stationary solution having a fixed number (Formula presented.) of nodal regions. We prove that the solution of (NLH) with initial value (Formula presented.) blows up in finite time if {pipe}λ -1{pipe} > 0 is sufficiently small and if p is sufficiently large. The proof is based on the analysis of the asymptotic behavior of (Formula presented.) and of the linearized operator (Formula presented.). © 2014 Springer Basel.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
