We prove by using an iteration argument some blow-up results for a semilinear damped wave equation in generalized Einstein–de Sitter spacetime with a time-dependent coefficient for the damping term and power nonlinearity. Then, we conjecture an expression for the critical exponent due to the main blow-up results, which is consistent with many special cases of the considered model and provides a natural generalization of Strauss exponent. In the critical case, we consider a non-autonomous and parameter dependent Cauchy problem for a linear ODE of second order, whose explicit solutions are determined by means of special functions’ theory.

Blow-up results for semilinear damped wave equations in Einstein–de Sitter spacetime

Palmieri A.
2021-01-01

Abstract

We prove by using an iteration argument some blow-up results for a semilinear damped wave equation in generalized Einstein–de Sitter spacetime with a time-dependent coefficient for the damping term and power nonlinearity. Then, we conjecture an expression for the critical exponent due to the main blow-up results, which is consistent with many special cases of the considered model and provides a natural generalization of Strauss exponent. In the critical case, we consider a non-autonomous and parameter dependent Cauchy problem for a linear ODE of second order, whose explicit solutions are determined by means of special functions’ theory.
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/11586/387809
 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??? 11
social impact