Firstly, my main question boils down to speaking about the initial conditions and boundary conditions.(adsbygoogle = window.adsbygoogle || []).push({});

I was given:

$$ u(0,y,t) = u(\pi,y,t) = u(x,0,t) = u(x,\pi,t) = 0 $$

but then the initial condition was:

$$ u(x,y,0) = 1 $$

Aren't the initial and boundary conditions inconsistent in such a case? For example, what is the value of ##u(0,0,0)##? Based on the boundary conditions, it should be 0, but based on the initial conditions, it should be 1, no? Why exactly is this okay, if it is okay?

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# Solving a PDE w/ given boundary and initial conditions

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