• DOI:10.1090/CONM/635
• Corpus ID: 2430482

Nonlinear Wave Equations

@inproceedings{Curtis2015NonlinearWE,
  title={Nonlinear Wave Equations},
  author={Christopher W. Curtis and Anton Dzhamay and Willy A. Hereman and Barbara Prinari},
  year={2015}
}

• C. Curtis, A. Dzhamay, +1 author B. Prinari
• Published 26 March 2015
• Mathematics

where := −∂2 t +∆ and u[0] := (u, ut)|t=0. The equation is semi-linear if F is a function only of u, (i.e. F = F (u)), and quasi-linear if F is also a function of the derivatives of u (i.e. F = F (u,Du), where D := (∂t,∇)). The goal is to use energy methods to prove local well-posedness for quasilinear equations with data (f, g) ∈ Hs × Hs−1 for large enough s, and then to derive Strichartz estimates to deal with semi-linear problems with data (f, g) ∈ Ḣ1 × L2. We begin, however, by deriving various conservation laws for solutions of wave equations.