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

Abstract

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.

Latex file, 22 pages

References in corpus (1)

• Existence and uniqueness results for a class of non linear models

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