On Blow-up Solutions of A Parabolic System Coupled in Both Equations and Boundary Conditions

يهتم هذا البحث بالحلول المنفجرة لنظام يتكون من معادلتي انتشارو رد الفعل مقترنتين في كلا من المعادلات والشروط الحدودية. لغرض فهم كيفية تاثير مقاطع رد العفل والشروط الحدودية على خواص الانفجار، تم القيام باشتقاق القيد السفلي والعلوي للانفجار. علاوة على ذلك، تمت دراسة مجموعة النقاط المنفجرة تحت شروط محددة.This paper is concerned with the blow-up solutions of a system of two reaction-diffusion equations coupled in both equations and boundary conditions. In order to understand how the reaction terms and the boundary terms affect the blow-up properties, the lower and upper blow-up rate estimates are derived. Moreover, the blow-up set under some restricted assumptions is studied

Blow-up Time for a Semilinear Heat Equation with a Gradient Term

We consider the semilinear Heat equation with a gradient term, which takes the form....... The full paper can be donwload using the link below

Multi-frequency scatter broadening evolution of pulsars - II. Scatter broadening of nearby pulsars

We present multi-frequency scatter broadening evolution of 29 pulsars observed with the LOw Frequency ARray (LOFAR) and Long Wavelength Array (LWA). We conducted new observations using LOFAR Low Band Antennae (LBA) as well as utilized the archival data from LOFAR and LWA. This study has increased the total of all multi-frequency or wide-band scattering measurements up to a dispersion measure (DM) of 150~pc\,cm$^{-3}$ by 60\%. The scatter broadening timescale ($\tau_{sc}$) measurements at different frequencies are often combined by scaling them to a common reference frequency of 1\,GHz. Using our data, we show that the $\tau_{sc}$--DM variations are best fitted for reference frequencies close to 200--300\,MHz, and scaling to higher or lower frequencies results in significantly more scatter in data. We suggest that this effect might indicate a frequency dependence of the scatter broadening scaling index ($\alpha$). However, a selection bias due to our chosen observing frequencies can not be ruled out with the current data set. Our data did not favour any particular model of the DM -- $\tau_{sc}$ relations, and we do not see a statistically significant break at the low DM range in this relation. The turbulence spectral index ($\beta$) is found to be steeper than that is expected from a Kolmogorov spectrum. This indicates that the local ISM turbulence may have a low wave-number cutoff or presence of large scale inhomogeneities in the line of sight to some of the reported pulsars.Comment: Accepted for publication in Ap

A Search for Pulsars in Steep Spectrum Radio Sources

We report on a time-domain search for pulsars in 44 steep spectrum radio sources originally identified from recent imaging surveys. The time-domain search was conducted at 327 MHz using the Ooty radio telescope, and utilized a semi-coherent dedispersion scheme retaining the sensitivity even for sub-millisecond periods up to reasonably high dispersion measures. No new pulsars were found. We discuss the nature of these steep spectrum sources and argue that majority of the sources in our sample should either be pulsars or a new category of Galactic sources. Several possibilities that could hinder detection of these sources as pulsars, including anomalously high scattering or alignment of the rotation and magnetic axes, are discussed in detail, and we suggest unconventional search methods to further probe these possibilities.Comment: Accepted for publication in Ap