Questions tagged [partial-differential-equations]

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Finite difference discretization of the Cauchy-Riemann PDEs

I made a forward fd-discretization of the Cauchy-Riemann PDEs but I am struggling to implement this in python. I have a quadratic mesh with heighτ = $2*\pi$. The dirichlet boundary conditions are at $...
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Optimal control of the gradient type PDE

I recently encountered the following optimal control problem. The purpose of the system is to find the parameter $x$ at which the maximum or minimum of the function $f$ a is reached. $x$ is unknown to ...
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Obtaining equation from real life

As I was studying about differential equation,then I got a question in my mind that we are taking out general solutions for a differential equation. Like for example - Q) $\frac{dy}{dx} = \left[\frac{...
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Finding characteristic time required to reach steady state in the pump equation

Consider the pump equation $$\rho \frac{\partial w}{\partial t} = K' + \frac{\mu}{r} \frac{\partial }{\partial r} \left(r \frac{\partial w}{\partial r} \right)$$ Subject to $w(r=R,t)=0$, $w(r=0,t)$ is ...
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Internal Tent Temperature

Here is the problem I am working on: "Consider a perfectly sealed polygonal tent with the sun directly overhead. The solar irradiance of a surface 90° to the sun’s rays is 1,000 W/m2. However, ...
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Is the viscosity solution of Hamilton-Jacobi equation of practical use in optimal control?

My understanding is, given an optimal control problem, one can show that the optimal cost satisfies a Hamilton-Jacobi PDE and use dynamic programming to figure out the optimal control. However, ...