Does Negative Divergence of Gradient Temperature Lead to the Laplace Equation?

range.rover · 2014-08-05T23:04:20+00:00

does negative divergence of gradient tempearature gives to lalace equation...? -div(∇T) = [∂^2T/∂x^2+∂^2T/∂y^2]

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...

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Thread 'Direction Fields and Isoclines'

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