In this paper we consider the problem of nonexistence of solutions for abstract evolution equations of the type Putt+Q(t)ut+A(t,u)=F(t,u), 0≤t<∞, where P and Q(t) are linear selfadjoint operators. The first theorem is an extension of earlier works of Levine [cf. SIAM J. Math. Anal. 5 (1974), 138-146], where the case where Q(t) is independent of t is treated. Secondly, the authors consider the case where Q(t,ut) is nonlinear and show that under certain assumptions the problem is essentially reduced to the case where A(t,u)=A(u) and F(t,u)=F(u), which has been treated by Levine and Serrin [Arch. Rational Mech. Anal. 137 (1997), 341-361].
Some remarks on the global nonexistence problem for nonautonomous abstract evolution equations
PUCCI, Patrizia;
1997
Abstract
In this paper we consider the problem of nonexistence of solutions for abstract evolution equations of the type Putt+Q(t)ut+A(t,u)=F(t,u), 0≤t<∞, where P and Q(t) are linear selfadjoint operators. The first theorem is an extension of earlier works of Levine [cf. SIAM J. Math. Anal. 5 (1974), 138-146], where the case where Q(t) is independent of t is treated. Secondly, the authors consider the case where Q(t,ut) is nonlinear and show that under certain assumptions the problem is essentially reduced to the case where A(t,u)=A(u) and F(t,u)=F(u), which has been treated by Levine and Serrin [Arch. Rational Mech. Anal. 137 (1997), 341-361].I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
