Problem: Let a be a positive twice differentiable function that is positive everywhere. Consider the partial differential equation: 4 = (ua(2)zz with Dirichlet Boundary conditions. Show that the weighted L norm of the solution (withrespect to the space variable) is decreasingon- increasing as t increases. What conclusion canwe draw from this result about the physical behavior of the system if the solution represents the temperature distribution on a rod? Problem: Let a be a positive twice differentiable function that is positive everywhere. Consider the partial differential equation: 4 = (ua(2)zz with Dirichlet Boundary conditions. Show that the weighted L norm of the solution (withrespect to the space variable) is decreasingon- increasing as t increases. What conclusion canwe draw from this result about the physical behavior of the system if the solution represents the temperature distribution on a rod