The given initial value problem and determine how the interval in which the solution exists depends on the initial value y 0 .

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Q3: Define the linear functional J: H(2) R by 1(v) = a(v. v) - L(v) Let u be the unique weak solution to a(u,v) = L(v) in H() and suppose that a(...) is a symmetric bilinear form on H(2) prove that 1- u is minimizer. 2- u is unique. 3- The minimizer J(u,) can be rewritten under algebraic form u Au-ub. J(u)=u'Au- Where A. b are repictively the stiffence matrix and the load vector

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Chapter 2.4, Problem 11P

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To solve: The given initial value problem and determine how the interval in which the solution exists depends on the initial value y0.

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