Solving a partial differential equation with separation of variables

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Scanned printed page showing Problem 1: a nonlinear one-dimensional heat equation system (NLP) with initial and boundary conditions, followed by the start of Problem 2 about Robin's boundary condition, with a handwritten scribble at the bottom right.

Scanned page of a math problem: a boxed system labelled (SSP) with -kΔu = f in R and k ∂u/∂n + αu = g on ∂R, followed by the note that f and g are given functions and α and k are positive constants, and the bold prompt 'Show that if (SSP) has a solution it is necessarily unique.'

Homework Equations


N/a


The Attempt at a Solution


Handwritten derivation on lined paper of a PDE boundary value problem, with boundary conditions w(0,t)=0 and w(L,t)=0 and equations involving integrals and partial derivatives.

Handwritten derivation on lined notebook paper of a Robin boundary value problem: -k del^2 u = f in R, k du/dn + alpha u = g on the boundary, with substitutions w = u - u_0, followed by integral identities using Green's theorem.


I am wondering if this is the right direction in solving this. any input would be great! Sorry for the messy handwriting!
 
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Welcome to PF!

Well the first problem with your post is posting images.

And the second problem with your post is it show two questions and some work done on paper.

Which question are you trying to solve and what page goes with what question?

My suggestion is to follow our homework template and type in what you've got so people can see it more clearly.

We have an advanced input editor that can provide latex support for entering your formulas.

This is probably why no one has responded yet as its hard to point out where you went wrong from an image of your work.
 

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