An existence result for dissipative nonhomogeneous hyperbolic equations via a minimization approach

TL;DR

This paper introduces a variational method to establish the existence of solutions for a broad class of dissipative nonhomogeneous hyperbolic PDEs, extending prior research on the De Giorgi approach to these equations.

Contribution

It develops a new variational framework for analyzing second order dissipative hyperbolic PDEs with source and linear terms, advancing the De Giorgi method in this context.

Findings

Proves existence of solutions for a class of hyperbolic PDEs.

Extends the De Giorgi approach to nonhomogeneous dissipative equations.

Provides a new variational technique for hyperbolic PDE analysis.

Abstract

We discuss a purely variational approach to the study of a wide class of second order nonhomogeneous dissipative hyperbolic PDEs. Precisely, we focus on the wave-like equations that present also a nonzero source term and a first-order-in-time linear term. The paper carries on the research program initiated in (Serra&Tilli'12), and developed in (Serra&Tilli'16), (Tentarelli&Tilli '18), on the De Giorgi approach to hyperbolic equations.