Introduction to Partial Differential Equations

1.Use the change of variable v(x,t):=v(x,t)-h(t)to convert the problem into a new problem with homogeneous boundary condition.

'1- In this problem we will learn a led'mique for transforming certain problems with iriomogeneous boundary conditions into problems with homogeneous boundary conditions. This will be done by a change of'variable that converts the irahomoge- ncous boundary oonditlon to a homogeneous one. The basic idea is that the bmmdary conditions can be made homogeneous by subtracting any known mction that satises them. {a} Consider the problem wait-urn {lei-nun~ 1:0 \"(1:0) = WEI] 1:011} = Hr} Use the change of variable cur} := 1111:] - km to convert the problem into a new problem 1with hmnogmeous boundary condilion. {11] Consider the problem v,=.i'vn