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This paper is concerned with an ideal polytropic model of non-viscous and heat-conductive gas in a one-dimensional half space. We focus our attention on the outflow problem when the flow velocity on the boundary is negative and we prove the stability of the viscous shock wave and its superposition with the boundary layer under some smallness conditions. Our waves occur in the subsonic area. The intrinsic properties of our system are more challenging in mathematical analysis, however, in the subsonic area, the lack of a boundary condition on the density provides us with a special manner for defining the shift for the viscous shock wave, and helps us to construct the asymptotic profiles successfully. New weighted energy estimates are introduced and the perturbations on the boundary are handled by some subtle estimates.

Passivation engineering has been identified as an effective strategy to eliminate the targeted interfacial defects for improving the efficiency and stability of perovskite solar cells (PSCs). Herein, 4-trifluorophenylammonium iodide (CF3PhAI) is presented as a multifunctional passivation agent to modify buried SnO2/perovskite and perovskite/hole transport layer (HTL) interfaces. Upon incorporation of CF3PhAI between SnO2and perovskite, CF3PhAI can chemically link to SnO2via Lewis coordination and electrostatic coupling, thereby effectively passivating under-coordinated Sn and filling the oxygen vacancy. Meanwhile, CF3PhAI helps anchor PbI2and organic cations (MA+/FA+) to control the crystallization of the perovskite. Consequently, reduced interfacial defects, homogeneous perovskite crystallites, and better energetic alignment can be simultaneously achieved. When CF3PhAI was further used to modify the perovskite/HTL interface, the fabricated PSCs yielded an impressive power conversion efficiency of 23.06% together with negligible J–Vhysteresis. The unencapsulated devices exhibited long-term stability in wet conditions (91.8% efficiency retention after 1000 h) due to the water-resistant CF3PhAI. We also achieved good light soaking stability, maintaining 86.1% of its initial efficiency after aging for 720 h. Overall, our finding provides a promising strategy for modifying the dual contact interfaces of PSCs toward improved efficiency and stability.

This article is concerned with the impermeable wall problem for an ideal poly-tropic model of non-viscous and heat-conductive gas in one-dimensional half space. It is shown that the 3-rarefaction wave is stable under some smallness conditions. The proof is given by an elementary energy method and the key point is to do the higher order derivative estimates with respect to tbecause of the less dissipativity of the system and the higher order derivative boundary terms.