This paper studies the global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with appropriate initial and mixed boundary conditions. Under some practicable regularity criteria on diffusion item and nonlinearity, we establish the local existence and uniqueness of classical solutions based on a contraction mapping. This local solution can be continued for all positive time by employing the methods of energy estimates, Lp-theory, and Schauder estimate of linear parabolic equations. A straightforward application of global existence result of classical solutions to a density-dependent diffusion model of in vitro glioblastoma growth is also presented.
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An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
Squaraine dyes gained significant attention as dye-sensitized solar cell (DSSCs) materials. In present study; we have studied the important parameters which influence the performance of DSSCs by considering the TiO2 clusters as acceptor material. We have investigated the structural, electro-optical and charge transport properties of six indole-based squaraine dyes (Cis-SQ1-SQ3 and Trans-SQ1-SQ3). The ground state geometries have been optimized by using density functional theory (DFT) then excitation energies and oscillator strengths were computed by time-dependent DFT in solvent. We shed light on the frontier molecular orbitals (highest occupied and lowest unoccupied molecular orbitals), electron injection (ΔGinject), relative electron injection (ΔG inject), electronic coupling constants (|VRP|), light harvesting efficiencies (LHE), short-circuit current density (Jsc) and open-circuit voltage (Voc). The ΔGinject, ΔG inject and |VRP| of six sensitizers have been compared with some previously studied sensitizers. The effect of donor (-OCH3) and acceptor (-COOH) groups has been investigated and discussed on said properties of interests. The Cis/Trans geometric effect has been studied on the structural parameters, absorption wavelengths, ΔGinject, |VRP|, LHE, Voc and factors affecting the Jsc. It has been discussed that which geometric isomer would be more favorable to enhance the performance of DSSCs.
In this approach, selective and sensitive 1,4-dioxane sensor probe was developed based on facile NiO@Nd<sub>2</sub>O<sub>3</sub> nanocomposites embedded GCE for the safety management of environment and health care fields at a large scale.
The regioselective production of alkenes from (thio)carbonates was calculated by MP2/6-31G(d) method via pyrolysis processes. Four (thio)carbonates were calculated in this paper. They are S-sec-butyl O-methyl thiocarbonate (I), O-sec-butyl S-methyl thiocarbonate (II), sec-butyl methyl thioncarbonate (III), and sec-butyl methyl dithiocarbonate (IV). Thirteen potential thermolysis routes were revealed for the pyrolysis of each substance, including nine routes to produce regioselective alkenes and four rearrangement/decompose alternatives. Among nine alkene generation routes, six-membered ring transition states via a two-step mechanism required the lowest energy, while the other routes exhibited higher energy barriers. The calculation results demonstrated an alkene distribution hierarchy of 1-butene [Formula: see text] E-butene [Formula: see text] Z-butene for substances I and II, and an order of E-butene [Formula: see text] 1-butene [Formula: see text] Z-butene for substances III and IV.
This review illustrates the recent developments in heterogeneous catalysis using mixed metal or mixed linker MOFs.