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We present the serendipitous radio-continuum discovery of a likely Galactic supernova remnant (SNR) G305.4–2.2. This object displays a remarkable circular symmetry in shape, making it one of the most circular Galactic SNRs known. Nicknamed Teleios due to its symmetry, it was detected in the new Australian Square Kilometre Array Pathfinder (ASKAP) Evolutionary Map of the Universe (EMU) radio–continuum images with an angular size of 1 320
$^{\prime\prime}$
$\times$1 260
$^{\prime\prime}$ and PA = 0
$^\circ$. While there is a hint of possible H
$\alpha$ and gamma-ray emission, Teleios is exclusively seen at radio–continuum frequencies. Interestingly, Teleios is not only almost perfectly symmetric, but it also has one of the lowest surface brightnesses discovered among Galactic SNRs and a steep spectral index of 
$\alpha$=–0.6
$\pm$0.3. Our best estimates from Hi studies and the 
$\Sigma$–D relation place Teleios as a type Ia SNR at a distance of either 
$\sim$2.2 kpc (near-side) or 
$\sim$7.7 kpc (far-side). This indicates two possible scenarios, either a young (under 1 000 yr) or a somewhat older SNR (over 10 000 yr). With a corresponding diameter of 14/48 pc, our evolutionary studies place Teleios at the either early or late Sedov phase, depending on the distance/diameter estimate. However, our modelling also predicts X-ray emission, which we do not see in the present generation of eROSITA images. We also explored a type Iax explosion scenario that would point to a much closer distance of 
$\lt$1 kpc and Teleios size of only 
$\sim$3.3 pc, which would be similar to the only known type Iax remnant SN1181. Unfortunately, all examined scenarios have their challenges, and no definitive Supernova (SN) origin type can be established at this stage. Remarkably, Teleios has retained its symmetrical shape as it aged even to such a diameter, suggesting expansion into a rarefied and isotropic ambient medium. The low radio surface brightness and the lack of pronounced polarisation can be explained by a high level of ambient rotation measure (RM), with the largest RM being observed at Teleios’s centre.
We present a re-discovery of G278.94+1.35a as possibly one of the largest known Galactic supernova remnants (SNRs) – that we name Diprotodon. While previously established as a Galactic SNR, Diprotodon is visible in our new Evolutionary Map of the Universe (EMU) and GaLactic and Extragalactic All-sky MWA (GLEAM) radio continuum images at an angular size of 
$3{{{{.\!^\circ}}}}33\times3{{{{.\!^\circ}}}}23$, much larger than previously measured. At the previously suggested distance of 2.7 kpc, this implies a diameter of 157
$\times$152 pc. This size would qualify Diprotodon as the largest known SNR and pushes our estimates of SNR sizes to the upper limits. We investigate the environment in which the SNR is located and examine various scenarios that might explain such a large and relatively bright SNR appearance. We find that Diprotodon is most likely at a much closer distance of 
$\sim$1 kpc, implying its diameter is 58
$\times$56 pc and it is in the radiative evolutionary phase. We also present a new Fermi-LAT data analysis that confirms the angular extent of the SNR in gamma rays. The origin of the high-energy emission remains somewhat puzzling, and the scenarios we explore reveal new puzzles, given this unexpected and unique observation of a seemingly evolved SNR having a hard GeV spectrum with no breaks. We explore both leptonic and hadronic scenarios, as well as the possibility that the high-energy emission arises from the leftover particle population of a historic pulsar wind nebula.
Well-posedness in time-weighted spaces of certain quasilinear (and semilinear) parabolic evolution equations 
$u'=A(u)u+f(u)$ is established. The focus lies on the case of strict inclusions 
$\mathrm{dom}(f)\subsetneq \mathrm{dom}(A)$ of the domains of the nonlinearities 
$u\mapsto f(u)$ and 
$u\mapsto A(u)$. Based on regularizing effects of parabolic equations it is shown that a semiflow is generated in intermediate spaces. In applications this allows one to derive global existence from weaker a priori estimates. The result is illustrated by examples of chemotaxis systems.
