We consider a semilinear wave equation with scale-invariant damping and mass and power nonlinearity. For this model we prove some global (in time) existence results in odd spatial dimension n, under the assumption that the multiplicative constants μ and ν^2 , which appear in the coefficients of the damping and of the mass terms, respectively, satisfy an interplay condition which makes the model somehow “wave-like”. Combining these global existence results with a recently proved blow-up result, we will find as critical exponent for the considered model the largest between suitable shifts of the Strauss exponent and of Fujita exponent, respectively. Besides, the competition among these two kind of exponents shows how the interrelationship between μ and ν^2 determines the possible transition from a “hyperbolic-like” to a “parabolic-like” model. Nevertheless, in the case n ≥ 3 we will restrict our considerations to the radial symmetric case.

Global Existence Results for a Semilinear Wave Equation with Scale-Invariant Damping and Mass in Odd Space Dimension

Palmieri A.
2019-01-01

Abstract

We consider a semilinear wave equation with scale-invariant damping and mass and power nonlinearity. For this model we prove some global (in time) existence results in odd spatial dimension n, under the assumption that the multiplicative constants μ and ν^2 , which appear in the coefficients of the damping and of the mass terms, respectively, satisfy an interplay condition which makes the model somehow “wave-like”. Combining these global existence results with a recently proved blow-up result, we will find as critical exponent for the considered model the largest between suitable shifts of the Strauss exponent and of Fujita exponent, respectively. Besides, the competition among these two kind of exponents shows how the interrelationship between μ and ν^2 determines the possible transition from a “hyperbolic-like” to a “parabolic-like” model. Nevertheless, in the case n ≥ 3 we will restrict our considerations to the radial symmetric case.
2019
978-3-030-10937-0
File in questo prodotto:
Non ci sono file associati a questo prodotto.

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/11586/387833
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 13
  • ???jsp.display-item.citation.isi??? ND
social impact