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.

arXiv comment21 pages; keywords: minimization, nonhomogeneous hyperbolic equations, dissipation, De Giorgi conjecture

References in corpus (2)

• De Giorgi's approach to hyperbolic Cauchy problems: the case of nonhomogeneous equations
• On the extensions of the De Giorgi approach to nonlinear hyperbolic equations

Cited by in corpus (4)

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• Stochastic PDEs via convex minimization
• Variational resolution of outflow boundary conditions for incompressible Navier-Stokes
• Newton's second law as limit of variational problems