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

摘要

We prove existence and uniqueness of solutions of a large class ofinitial-boundary-value problems characterized by a quasi-linear third orderequation (the third order term being dissipative) on a finite space intervalwith Dirichlet, Neumann or pseudoperiodic boundary conditions. The classincludes equations arising in superconductor theory, such as a well-knownmodified sine-Gordon equation describing the Josephson effect, and in thetheory of viscoelastic materials.