NLWE WITH A SPECIAL SCALE INVARIANT DAMPING IN ODD SPACE DIMENSION

Author(s)

D'Abbicco, Marcello ^[1] ; Lucente, Sandra ^[2]

Affiliation

^[1] Univ Sao Paulo, Dept Comp & Matemat, FFCLRP, Av Bandeirantes 3900, BR-14040901 Ribeirao Preto, SP - Brazil

^[2] Univ Bari, Dept Math, I-70125 Bari, BA - Italy

• Document type: Journal article
• Source: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; n. SI, p. 312-319, 2015.
• Web of Science Citations: 3

Abstract

Let p(0)(k) be the critical Strauss exponent for the nonlinear wave equation u(tt) - Delta u = vertical bar u vertical bar(p) in R-t x R-x(k).In this note we prove global existence for small data radial solutions to v(tt) - Delta v + 2(1 + t)(-1) v(t) = vertical bar v vertical bar(p) in R-t x R-x(n), provided that p > p(0)(n + 2) and n >= 5 is odd. This result is a counterpart of the non-existence result for p is an element of (1, p(0)(n + 2)] in {[}2]. In particular we show that the scale invariant damping term 2(1 + t)(-1) u(t) shifts by 2 the critical exponent of NLWE. (AU)

• FAPESP's process: 13/15140-2 - Decay estimates for semilinear hyperbolic equations
• Grantee: Marcello Dabbicco
• Support Opportunities: Research Grants - Young Investigators Grants
• FAPESP's process: 14/02713-7 - Decay estimates for semilinear hyperbolic equations
• Grantee: Marcello Dabbicco
• Support Opportunities: Scholarships in Brazil - Young Researchers