A maximum principle for bounded solutions of the telegraph equation in space dimension three

Mawhin, Jean;Ortega, R.;Robles-Perez, AM
(2002) Comptes rendus - Mathématique — Vol. 334, n° 12, p. 1089-1094 (2002)

Files

pdfdocument.pdf
  • Restricted Access
  • Adobe PDF
  • 71.41 KB
Request a copy

Details

Authors
  • Mawhin, JeanUCLouvain
    Author
  • Ortega, R.
    Author
  • Robles-Perez, AM
    Author
Abstract
A maximum principle is proved for the weak solutions u is an element of L-infinity(R x T-3) of the telegraph equation u(tt) - Delta(x)u + cu(t) + lambda(u) = f(t, x), in space dimension three, when c > 0, lambda is an element of (0, c(2)/4] and f is an element of L-infinity (R x T-3) (Theorem 1). The result is extended to a solution and a forcing belonging to a suitable space of bounded measures (Theorem 2). Those results provide a method of upper and lower solutions for the semilinear equation u(tt) - Delta(x)u + cut = F(t, x, it). (C) 2002 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.
Affiliations

Citations

  • APA
  • Chicago
  • FWB

Mawhin, J., Ortega, R., & Robles-Perez, A. (2002). A maximum principle for bounded solutions of the telegraph equation in space dimension three. Comptes rendus - Mathématique, 334(12), 1089-1094. https://doi.org/10.1016/S1631-073X(02)02406-8 (Original work published 2002)