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

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.