Asymptotic behavior of type I blowup solutions to a parabolic-elliptic system of drift-diffusion type

A Cauchy problem for a parabolic-elliptic system of drift-di usion type is considered. The problem is formally of the form Ut = r (rU Ur( ) 1U): This system describes a mass-conserving aggregation phenomenon including gravitational collapse and bacterial chemotaxis. Our concern is the asymptotic behavior of blowup solutions when the blowup is type I in the sense that its blowup rate is the same as the corresponding ordinary di erential equation yt = y2 (up to a multiple constant). It is shown that all type I blowup is asymptotically (backward) self-similar provided that the solution is radial, nonnegative when the blowup set is a singleton and the space dimension is greater than or equal to three. 2000 Mathematics Subject Classi cation. 35K55, 35K57, 92C17.

Malignant Triton tumor in the retroperitoneal space associated with neurofibromatosis type 1: a case study

We report an extremely rare case of malignant Triton tumor developing in the retroperitoneal space in a patient with neurofibromatosis type 1. A 21-year old man who had been diagnosed with neurofibromatosis type 1 was admitted to our hospital with the chief complaint of a palpable abdominal mass. Abdominal computed tomography revealed a huge heterogeneous tumor measuring approximately 17 cm in diameter occupying the left retroperitoneal space, and numerous metastatic lesions between the left psoas muscle and the left thigh with dissolution of the left hip joint. After the diagnosis of a retroperitoneal malignant neurogenic tumor, resection of the tumor with reconstruction of the abdominal aorta was conducted, followed by postoperative transarterial infusion chemotherapy. The histopathological diagnosis was malignant peripheral nerve sheath tumor with rhabdomyosarcomatous differentiation, namely malignant Triton tumor. Postoperative chemotherapy was in vain and the patient died 14 months after the surgery as a result of lung metastasis