# Questions tagged [heat-equation]

For questions related to the solution and analysis of the heat equation.

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### Derivative of integral representation of Greens Function

I am interested in taking the differentiation of an integral representation containing the fundamental solution of the heat equation, hence the Greens function. The equation of interest I want to ...
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### Laplace equation with certain boundary conditions

I'm trying to solve the equation $u_{xx}+u_{yy} = 0$ on $[0,1] \times [0,\pi]$ with conditions $u(x,0)=u(x,\pi)=u(0,t) = 0$ and $u(1,t) = f(t).$ Is this the right method? I split $u = X(x)Y(y)$ then I ...
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### Which methods are applicable to solve problem of heat conduction on the surface of ball? [closed]

The problem is of heat conduction on the surface of ball. The surface of the ball is given as $r^2=x^2+y^2+z^2=R^2$ at zero temperature and initial temperature is $f(x)$? I also want to model the ...
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### Passing derivative through integral of a convolution

I'm trying to solve an exercise on Folland's book of real analysis on the part of fourier transforms and its applications on PDE's, when working with the heat equation one may show that given the heat ...
1answer
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### Is the heat equation (e.g. 2D) solvable without boundary conditions? Or are the boundary conditions always present?

Is the heat equation (e.g. 2D) solvable without boundary conditions? Or are the boundary conditions always present? I've been puzzled a bit, since it seems that w/o boundary conditions there's no ...
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### Separation of Variables Hiccup

Find the temperature $u(x,\ t)$ in a unit length rod modeled by $u_t = 4u_{xx}$ $u(0,\ t) = 0$ $u(1,\ t) = 0$ $u(x,\ 0) = x - x^2$ Breaking out the steady-state temperature, \$u(x,\ t) = s(x) + v(x,\ ...