Existence and blow-up of solution of Cauchy problem for the generalized damped multidimensional Boussinesq equation

AbstractWe consider the existence, both locally and globally in time, and the blow-up of solutions for the Cauchy problem of the generalized damped multidimensional Boussinesq equation

On Global Solutions for the Cauchy Problem of a Boussinesq-Type Equation

We will give conditions which will guarantee the existence of global weak solutions of the Boussinesq-type equation with power-type nonlinearity || and supercritical initial energy. By defining new functionals and using potential well method, we readdressed the initial value problem of the Boussinesq-type equation for the supercritical initial energy case

On the Decay of Solutions for a Nonlinear Petrovsky Equation

Under suitable conditions decay estimates of the solution are proved by using Nakaos inequality

Local Well-Posedness for a Generalized Integrable Shallow Water Equation with Strong Dispersive Term

In this paper, we consider a kind of new nonlinear dispersive wave equation, which is generalized integrable shallow water equation with strong dispersive term. Applying Kato’s semigroup approch, we obtained local well-posedness of Cauchy problem for the generalized integrable shallow water equation with strong dispersive term in Sobolev space (Hs,s \u3e (3/2))

Analysis of PTEN Gene Mutations in a Turkish Patient with Cowden Syndrome

Cowden syndrome (CS), an autosomal dominant disorder, is associated with germline mutations of the PTEN (phosphatase, tensin homolog, deleted on chromosome TEN) gene. PTEN mutations were linked to several human neoplasms. Clinical diagnosis has been based on Consortium criteria, but detection of mutations in the PTEN gene has importance in accurate diagnosis. This article presents a female patient with classic features of the syndrome and gives the result of first PTEN mutation analysis result in a Turkish CS patient. The patient, who suffered from trichilemmomas, papillomatous lesions, lipomas, thyroid lesions, gastrointestinal hamartomas, and fibrocystic disease of the breast, is consistent with the diagnostic criteria of CS. The exons and intron/exon boundaries of the PTEN gene were analyzed by polymerase chain reaction and direct sequencing. We analyzed the clinical features and DNA in a Turkish patient with CS. We found a single-nucleotide substitution in the splicing acceptor site of intron 5 of the PTEN gene (IVS5-2A > C). It is not clear whether which types of PTEN mutations are responsible for particular phenotypes. This germline PTEN mutation, IVS5-2A -> C, has been reported once before, but the clinical features differ from our patient. Also, this is the first reported PTEN mutation from Turkey