Table 1.
Open in new tab

Examples of three types of PIs on 1D heat equations (Ω = [− 1, 1]).

PDE formulaType of PIPI θPI space Θ
∂tu = κΔu, u(±1, t) = 0Spatiotemporal invariantκ[0, 1]
∂tu = 0.1Δu + f(x), u(±1, t) = 0Temporal invariantf(x){a sin (x): a ∈ [0, 1]}
∂tu = 0.1Δu, u(±1, t) = cBoundary invariantc[−1, 1]
PDE formulaType of PIPI θPI space Θ
∂tu = κΔu, u(±1, t) = 0Spatiotemporal invariantκ[0, 1]
∂tu = 0.1Δu + f(x), u(±1, t) = 0Temporal invariantf(x){a sin (x): a ∈ [0, 1]}
∂tu = 0.1Δu, u(±1, t) = cBoundary invariantc[−1, 1]
Table 1.
Open in new tab

Examples of three types of PIs on 1D heat equations (Ω = [− 1, 1]).

PDE formulaType of PIPI θPI space Θ
∂tu = κΔu, u(±1, t) = 0Spatiotemporal invariantκ[0, 1]
∂tu = 0.1Δu + f(x), u(±1, t) = 0Temporal invariantf(x){a sin (x): a ∈ [0, 1]}
∂tu = 0.1Δu, u(±1, t) = cBoundary invariantc[−1, 1]
PDE formulaType of PIPI θPI space Θ
∂tu = κΔu, u(±1, t) = 0Spatiotemporal invariantκ[0, 1]
∂tu = 0.1Δu + f(x), u(±1, t) = 0Temporal invariantf(x){a sin (x): a ∈ [0, 1]}
∂tu = 0.1Δu, u(±1, t) = cBoundary invariantc[−1, 1]
Close
This Feature Is Available To Subscribers Only

Sign In or Create an Account

Close

This PDF is available to Subscribers Only

View Article Abstract & Purchase Options

For full access to this pdf, sign in to an existing account, or purchase an annual subscription.

Close