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In this paper, we consider a mathematical model motivated by the studies of coral broadcast spawning { ∂ t n + u ⋅ ∇ n − Δ n = − χ ∇ ⋅ (n ∇ c) + n − ϵ n q ∂ t c + u ⋅ ∇ c − Δ c = − c + n in R d × R + , where d = 2 , 3 , ϵ > 0 , and q ≥ 2. We establish global-in-time well-posedness and boundedness of the solution to the Cauchy problem of this system by developing local-in-space estimates. The crux point of our proof depends intensely on localization in the space of solutions induced by "local effect" of the L ∞ (R d) -norm. [ABSTRACT FROM AUTHOR]

Establishing control over a mission to explore space is still one of the most difficult tasks. In order to achieve such mission control, we need communications into space through the transmission and reception of radio signals. To improve communication conditions, we propose a tracking system to locate space gadgets and transmit signals at minimum distances to reduce free space attenuation. We propose the case of a satellite sent off to the Moon or Mars, namely points where tracking devices can no longer reach them. In this paper, we discuss the methods and strategies to carry out this idea. The fingerprint of magnetic and gravitational fields can give us information to differentiate the quantity of electromagnetic waves that are received at a point in space in three dimensions. Each planet has specific characteristics, including a field around the planet, whether magnetic, electrical or otherwise, that protects its surface. The use of a spectrometer of masses allows us to identify the neighboring magnetic field as well as the compositions of celestial bodies and is a clear solution for the observation and monitoring of a planet. Additionally, the use of an oscillator is proposed to enhance the spectrometer. In conjunction with the use of a magnetometer, we can obtain an accurate measurement of the field of a celestial body, magnetic or not, and its composition. In addition, with the integration of an accelerometer, the altitude will be transformed into speed data, and to analyze its variation, we turn these data into gravitational force and define if the satellite is closer to the atmosphere of the celestial body. Attached to the sensing stage, a network of SatComs will be used to amplify the received signal and reach the ground station. Two SatComs per orbit will be positioned at specific Lagrange points of the celestial body.