23 research outputs found
Existence and nonexistence of global solutions for time-dependent damped NLS equations
We investigate the Cauchy problem for the nonlinear Schr\"odinger equation
with a time-dependent linear damping term. Under non standard assumptions on
the loss dissipation, we prove the blow-up in the inter-critical regime, and
the global existence in the energy subcritical case. Our results generalize and
improve the ones in [9, 11, 21].Comment: To appear in Communications on Pure and Applied Analysi
Blow-up and lifespan estimate for the generalized tricomi equation with the scale-invariant damping and time derivative nonlinearity on exterior domain
The article is devoted to investigating the initial boundary value problem
for the damped wave equation in the scale-invariant case with time-dependent
speed of propagation on the exterior domain. By presenting suitable multipliers
and applying the test-function technique, we study the blow-up and the lifespan
of the solutions to the problem with derivative-type nonlinearity
$ \d u_{tt}-t^{2m}\Delta u+\frac{\mu}{t}u_t=|u_t|^p, \quad \mbox{in}\
\Omega^{c}\times[1,\infty), $
that we associate with appropriate small initial data