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

Author

Maan A. Rasheed

Subjects
General Computer Science, General Mathematics, Science, 010102 general mathematics, Mathematical analysis, Mathematics::Analysis of PDEs, General Physics and Astronomy, Rection-Diffusion equation, Blow-up set, Blow-up rate estimate, Comparison principle, Radial function, General Chemistry, 01 natural sciences, Agricultural and Biological Sciences (miscellaneous), General Biochemistry, Genetics and Molecular Biology, 010101 applied mathematics, Parabolic system, Mathematics::Algebraic Geometry, Boundary value problem, 0101 mathematics, Mathematics
Abstract

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.

Published
2021

2. A Generalization of t-Practical Numbers

Author

saad abood baddai

Subjects
Discrete mathematics, General Computer Science, Generalization, General Mathematics, Bound for the t-practical numbers, Existence of t-practical numbers in an interval, Practical numbers, t-practical numbers, 010102 general mathematics, General Physics and Astronomy, General Chemistry, 01 natural sciences, Agricultural and Biological Sciences (miscellaneous), General Biochemistry, Genetics and Molecular Biology, 0103 physical sciences, lcsh:Q, 010307 mathematical physics, 0101 mathematics, lcsh:Science, Mathematics
Abstract

This paper generalizes and improves the results of Margenstren, by proving that the number of -practical numbers which is defined by has a lower bound in terms of . This bound is more sharper than Mangenstern bound when Further general results are given for the existence of -practical numbers, by proving that the interval contains a -practical for all

Published
2020