TY - JOUR
TI - Rigorous Numerics for PDEs with Indefinite Tail: Existence of a Periodic Solution of the Boussinesq Equation with Time-dependent Forcing
AU - Czechowski, Aleksander
AU - Zgliczyński, Piotr
TI - Rigorous Numerics for PDEs with Indefinite Tail: Existence of a Periodic Solution of the Boussinesq Equation with Time-dependent Forcing
AB - 
	We consider the Boussinesq PDE perturbed by a time-dependent forcing. Even though there is no smoothing effect for arbitrary smooth initial data, we are able to apply the method of self-consistent bounds to deduce the existence of smooth classical periodic solutions in the vicinity of 0. The proof is non-perturbative and relies on construction of periodic isolating segments in the Galerkin projections.
VL - 2015
IS - Volume 24
PY - 2016
SN - 1732-3916
C1 - 2083-8476
SP - 143
EP - 158
DO - 10.4467/20838476SI.15.014.3486
UR - https://ejournals.eu/en/journal/schedae-informaticae/article/rigorous-numerics-for-pdes-with-indefinite-tail-existence-of-a-periodic-solution-of-the-boussinesq-equation-with-time-dependent-forcing
KW - Boussinesq equation
KW - ill-posed PDEs
KW - periodic solutions
KW - isolating segments