Blow-up and lifespan estimate for the generalized tricomi equation with the scale-invariant damping and time derivative nonlinearity on exterior domain

The article is devoted to investigating the initial boundary value problem for the damped wave equation in the scale-invariant case with time-dependent speed of propagation on the exterior domain. By presenting suitable multipliers and applying the test-function technique, we study the blow-up and the lifespan of the solutions to the problem with derivative-type nonlinearity $ \d u_{tt}-t^{2m}\Delta u+\frac{\mu}{t}u_t=|u_t|^p, \quad \mbox{in}\ \Omega^{c}\times[1,\infty), $ that we associate with appropriate small initial data

Auricular mucormycosis complicated by parotid abscess and facial paralysis: A very rare case report

Abstract Mucormycosis is a serious and relatively rare invasive fungal infection. The rhino‐orbito‐cerebral localization is the most frequent. Other localizations have been reported including: cutaneous, pulmonary, disseminated, gastrointestinal, and miscellaneous. Mucormycosis of external ear with facial palsy is extremely rare and only few cases have been reported in the literature. We describe a case of mucormycosis of the external and middle in a 44‐years‐old diabetic patient which had a very aggressive form of necrotic infection of the ear auricle complicated by parotid abscess, facial, and vagal nerve paralysis. Auricular mucormycosis was suspected and the diagnosis was established after biopsy and histological examination. The patient was treated immediately with intravenous amphotericin B followed by extensive surgical debridement of the necrotic lesions. The patient responded well to the treatment despite the persistence of facial palsy