Mixing
How do I find equilibrium points of a partial differential equation?
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How do i find the critical points of this fourth order differential equation.
begin{equation} Dleft(frac{d^4w}{dx^4}+frac{d^4w}{dy^4}+frac{d^4w}{dz^4}right)+(rho_m-rho_c)gw=q-Pleft(frac{d^2w}{dx^2}+frac{d^2w}{dy^2}+frac{d^2w}{dz^2}right). label{bilaplaciano31} end{equation}
D, P, q, $rho_m$, $rho_c$, g are constants.
The boundary conditions are free.
Does anyone know how to get all the critical values for this problem? Thanks.
ordinary-differential-equations
asked Jan 10 at 15:59
carlos gomezcarlos gomez
11
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add a comment |
$begingroup$
How do i find the critical points of this fourth order differential equation.
begin{equation} Dleft(frac{d^4w}{dx^4}+frac{d^4w}{dy^4}+frac{d^4w}{dz^4}right)+(rho_m-rho_c)gw=q-Pleft(frac{d^2w}{dx^2}+frac{d^2w}{dy^2}+frac{d^2w}{dz^2}right). label{bilaplaciano31} end{equation}
D, P, q, $rho_m$, $rho_c$, g are constants.
The boundary conditions are free.
Does anyone know how to get all the critical values for this problem? Thanks.
ordinary-differential-equations
asked Jan 10 at 15:59
carlos gomezcarlos gomez
11
$endgroup$
1
$begingroup$
What have you tried so far?
$endgroup$
– user3482749
Jan 10 at 16:00
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I solve the equation with finite differences placing a sinusoidal load distribution, obtaining an approximate solution. I also thought about finding the critical values of begin{equation} Dw''''+(rho_m-rho_c)gw=q-Pw''. label{bilaplaciano31} end{equation} overleaf.com/read/hcpnbdcqctdh to simplify the problem but I'm not sure if it's okay
$endgroup$
– carlos gomez
Jan 10 at 16:19
add a comment |
$begingroup$
How do i find the critical points of this fourth order differential equation.
begin{equation} Dleft(frac{d^4w}{dx^4}+frac{d^4w}{dy^4}+frac{d^4w}{dz^4}right)+(rho_m-rho_c)gw=q-Pleft(frac{d^2w}{dx^2}+frac{d^2w}{dy^2}+frac{d^2w}{dz^2}right). label{bilaplaciano31} end{equation}
D, P, q, $rho_m$, $rho_c$, g are constants.
The boundary conditions are free.
Does anyone know how to get all the critical values for this problem? Thanks.
ordinary-differential-equations
asked Jan 10 at 15:59
carlos gomezcarlos gomez
11
$endgroup$
How do i find the critical points of this fourth order differential equation.
begin{equation} Dleft(frac{d^4w}{dx^4}+frac{d^4w}{dy^4}+frac{d^4w}{dz^4}right)+(rho_m-rho_c)gw=q-Pleft(frac{d^2w}{dx^2}+frac{d^2w}{dy^2}+frac{d^2w}{dz^2}right). label{bilaplaciano31} end{equation}
D, P, q, $rho_m$, $rho_c$, g are constants.
The boundary conditions are free.
Does anyone know how to get all the critical values for this problem? Thanks.
ordinary-differential-equations
ordinary-differential-equations
asked Jan 10 at 15:59
carlos gomezcarlos gomez
11
asked Jan 10 at 15:59
carlos gomezcarlos gomez
11
asked Jan 10 at 15:59
carlos gomezcarlos gomez
11
asked Jan 10 at 15:59
carlos gomezcarlos gomez
11
asked Jan 10 at 15:59
carlos gomezcarlos gomez
11
11
1
$begingroup$
What have you tried so far?
$endgroup$
– user3482749
Jan 10 at 16:00
$begingroup$
I solve the equation with finite differences placing a sinusoidal load distribution, obtaining an approximate solution. I also thought about finding the critical values of begin{equation} Dw''''+(rho_m-rho_c)gw=q-Pw''. label{bilaplaciano31} end{equation} overleaf.com/read/hcpnbdcqctdh to simplify the problem but I'm not sure if it's okay
$endgroup$
– carlos gomez
Jan 10 at 16:19
add a comment |
1
$begingroup$
What have you tried so far?
$endgroup$
– user3482749
Jan 10 at 16:00
$begingroup$
I solve the equation with finite differences placing a sinusoidal load distribution, obtaining an approximate solution. I also thought about finding the critical values of begin{equation} Dw''''+(rho_m-rho_c)gw=q-Pw''. label{bilaplaciano31} end{equation} overleaf.com/read/hcpnbdcqctdh to simplify the problem but I'm not sure if it's okay
$endgroup$
– carlos gomez
Jan 10 at 16:19
1
1
$begingroup$
What have you tried so far?
$endgroup$
– user3482749
Jan 10 at 16:00
$begingroup$
What have you tried so far?
$endgroup$
– user3482749
Jan 10 at 16:00
$begingroup$
I solve the equation with finite differences placing a sinusoidal load distribution, obtaining an approximate solution. I also thought about finding the critical values of begin{equation} Dw''''+(rho_m-rho_c)gw=q-Pw''. label{bilaplaciano31} end{equation} overleaf.com/read/hcpnbdcqctdh to simplify the problem but I'm not sure if it's okay
$endgroup$
– carlos gomez
Jan 10 at 16:19
$begingroup$
I solve the equation with finite differences placing a sinusoidal load distribution, obtaining an approximate solution. I also thought about finding the critical values of begin{equation} Dw''''+(rho_m-rho_c)gw=q-Pw''. label{bilaplaciano31} end{equation} overleaf.com/read/hcpnbdcqctdh to simplify the problem but I'm not sure if it's okay
$endgroup$
– carlos gomez
Jan 10 at 16:19
add a comment |
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$begingroup$
What have you tried so far?
$endgroup$
– user3482749
Jan 10 at 16:00
$begingroup$
I solve the equation with finite differences placing a sinusoidal load distribution, obtaining an approximate solution. I also thought about finding the critical values of begin{equation} Dw''''+(rho_m-rho_c)gw=q-Pw''. label{bilaplaciano31} end{equation} overleaf.com/read/hcpnbdcqctdh to simplify the problem but I'm not sure if it's okay
$endgroup$
– carlos gomez
Jan 10 at 16:19