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We establish the existence of a global solution to a regular reflection of a shock hitting a ramp for the pressure gradient system of equations. The set-up of the reflection is the same as that of Mach’s experiment for the compressible Euler system, i.e., a straight shock hitting a ramp. We assume that the angle of the ramp is close to 90 degrees. The(More)
We present a global solution to a Riemann problem for the pressure gradient system of equations. The Riemann problem has initially two shock waves and two contact discontinuities. The angle between the two shock waves is set initially to be close to 180 degrees. The solution has a shock wave that is usually regarded as a free boundary in the self-similar(More)
Classical self-similar solutions to the interaction of two arbitrary planar rarefaction waves for the polytropic Euler equations in two space dimensions are constructed. The binary interaction represents a major type of interaction in the two-dimensional Riemann problems, and includes in particular the classical problem of the expansion of a wedge of gas(More)
We establish the existence of a smooth solution in its elliptic region in the self-similar plane to the pressure-gradient system arisen from the wave-particle splitting of the two-dimensional compressible Euler system of equations. The pressure-gradient system takes the form ρut+px = 0, ρvt+ py = 0, ρEt + (up)x + (vp)y = 0. Here (u, v) is the velocity, ρ is(More)
HYPOTHESIS Spiral ganglion neurons (SGN) in the Phex male mouse, a murine model of postnatal endolymphatic hydrops (ELH) undergo progressive deterioration reminiscent of human and other animal models of ELH with features suggesting apoptosis as an important mechanism. BACKGROUND Histologic analysis of the mutant's cochlea demonstrates ELH by postnatal Day(More)
Transporting epithelial cells build apical microvilli to increase membrane surface area and enhance absorptive capacity. The intestinal brush border provides an elaborate example with tightly packed microvilli that function in nutrient absorption and host defense. Although the brush border is essential for physiological homeostasis, its assembly is poorly(More)
We report a novel mutation (erlong, erl) of the cadherin 23 (Cdh23) gene in a mouse model for DFNB12 characterized by progressive hearing loss beginning from postnatal day 27 (P27). Genetic and sequencing analysis revealed a 208 T >C transition causing an amino-acid substitution (70S-P). Caspase expression was upregulated in mutant inner ears. Hearing was(More)