Derivation of the spatio-temporal model equations for the thermoacoustic   resonator
  We derive the model equations describing the thermoacoustic resonator, that is, an acoustical resonator containing a viscous medium inside. Previous studies on this system have addressed this sytem in the frame of the plane-wave approximation, we extend the previous model to by considering spatial effects in a large aperture resonator. This model exhibits pattern formation and localized structures scenario. 
Isabel Perez-Arjona, Victor J. Sanchez-Morcillo and German de   Valcarcel