def
definition
def or abbrev
duhamelKernelIntegral
show as:
view Lean formalization →
formal statement (Lean)
655noncomputable def duhamelKernelIntegral (ν : ℝ) (F : ℝ → FourierState2D) : ℝ → FourierState2D :=
proof body
Definition body.
656 fun t k => -∫ s in (0 : ℝ)..t, (heatFactor ν (t - s) k) • (F s k)
657
658/-- Hypothesis (at fixed `t,k`): the Duhamel-kernel integrands satisfy the assumptions of dominated
659convergence, so the corresponding interval integrals converge. -/
used by (12)
-
duhamelRemainderOfGalerkin_kernel -
galerkin_duhamelKernel_identity -
nsDuhamelCoeffBound_galerkinKernel -
nsDuhamelCoeffBound_galerkinKernel_of_forcing -
nsDuhamelCoeffBound_kernelIntegral -
nsDuhamelCoeffBound_kernelIntegral_of_forcing -
nsDuhamel_of_forall_kernelIntegral -
nsDuhamel_of_forall_kernelIntegral_of_forcing -
tendsto_duhamelKernelIntegral_of_dominated_convergence -
rs_implies_global_regularity_2d_nsDuhamelCoeffBound_galerkinKernel -
rs_implies_global_regularity_2d_nsDuhamelCoeffBound_galerkinKernel_of_forcing -
rs_implies_global_regularity_2d_nsDuhamelCoeffBound_galerkinKernel_of_forcingHyp