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

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 in...

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Bibliographic Details
Published in:Journal of Differential Equations 2019-04, Vol.266 (8), p.5185-5208
Main Authors: Tentarelli, Lorenzo, Tilli, Paolo
Format: Article
Language:English
Subjects:
De Giorgi conjecture
Dissipation
Minimization
Nonhomogeneous hyperbolic equations
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Summary: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 [14], and developed in [15,21], on the De Giorgi approach to hyperbolic equations.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2018.10.023