1205.2582 (Monica De Angelis et al.)

Existence and uniqueness of solutions of a class of 3rd order
dissipative problems with various boundary conditions describing the
Josephson effect    [PDF]

Monica De Angelis, Gaetano Fiore

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.

View original: http://arxiv.org/abs/1205.2582