In this paper, we derive some sufficient second order optimality conditions for control problems of partial differential equations (PDEs) when the cost functional does not involve the usual quadratic term for the control or higher nonlinearities for it. Though not always, in this situation the optimal control is typically bang-bang. Two different control problems are studied. The second differs...

The Big Bang Model is a widely accepted theory for the origin and evolution of our universe. It postulates that ∼ 12−14 billion years ago, a hot and dense plasma of quarks and gluons (QGP) was produced a few micro seconds after the “big bang”. A pervading uniform glow of cold cosmic microwave background provides an unequivocal signature for the subsequent expansion from this hot and dense state...