This paper is devoted to study the well-posedness and the asymptotic behavior of a population equation with diffusion in L^1. The death and birth rates depend on the age and the spatial variable. Here we allow the birth process to depend also on some modified delay. This paper is a continuation of the studies done by Nickel, Rhandi and Schnaubelt in [28, 32, 33] and Fragnelli, Maniar, Piazzera and Tonetto in [15, 21, 29, 30]
In the title molecule, C13H13N3O, the isoxazole ring is inclined to the benzimidazole ring at a dihedral angle of 69.28 (14)°. In the crystal, N—H...N hydrogen bonds between neighboring benzimidazole rings form chains along the a-axis direction. Hirshfeld surface analysis indicates that the most important contributions to the crystal packing are from H...H (48.8%), H...C/C...H (20.9%) and H...N/N...H (19.3%) interactions. The optimized structure calculated using density functional theory at the B3LYP/6–311 G(d,p) level is compared with the experimentally determined structure in the solid state. The calculated highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy gap is 4.9266 eV.
This paper studies a time discretization for a doubly nonlinear parabolic equation related to the p(x)-Laplacian by using Euler-forward scheme. We investigate existence, uniqueness, and stability questions and prove existence of the global compact attractor.
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