Jacobi equation for field theories and a geometric variational description of dissipation

TL;DR

This paper provides a geometric framework for Jacobi equations in first-order Lagrangian field theories and introduces a variational approach to dissipative field theories using a modified prolongation.

Contribution

It introduces a geometric description of Jacobi equations in field theories and develops a variational formulation for dissipative systems via a modified prolongation.

Findings

Geometric description of Jacobi equations in field theories

Variational formulation for dissipative field theories

Use of $k$-cosymplectic formulation

Abstract

In this paper we give a geometric description of the Jacobi equations associated to a first-order Lagrangian field theory using a prolongation of the Lagrangian $L$ on a $k$-cosymplectic formulation. Moreover, using an appropriate modification of the prolonged Lagrangian, we obtain a variational formulation of field theories with dissipation.