Existence and uniqueness of solutions of a class of 3rd order   dissipative problems with various boundary conditions describing the   Josephson effect
  We prove existence and uniqueness of solutions of a large class of initial-boundary-value problems characterized by a quasi-linear third order equation (the third order term being dissipative) on a finite space interval with Dirichlet, Neumann or pseudoperiodic boundary conditions. The class includes equations arising in superconductor theory, such as a well-known modified sine-Gordon equation describing the Josephson effect, and in the theory of viscoelastic materials. 
Monica De Angelis, Gaetano Fiore
math-ph cond-mat.supr-con math.MP