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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2003 • Question 4

Question

Math 6420 • PDE Fall 2003 • Question 4

Find the weak formulation for the boundary value problem \[ u''-\delta (x)u=1,\qquad u(-1)=u(1)=0, \tag {0.1} \] and then solve the problem. Verify that your solution is a weak solution. Why is it not a strong solution?

Raw LaTeX

Find the weak formulation for the boundary value problem
\[
  u''-\delta(x)u=1,\qquad u(-1)=u(1)=0,
\tag{0.1}
\]
and then solve the problem. Verify that your solution is a weak solution. Why is it not a
strong solution?

Topic Tags

Boundary Value Problems Distributions and Weak Solutions Fundamental Solutions Sobolev Spaces and Energy Estimates