In this paper, we establish some important results for the impulsive wave equation. We begin by proving the existence of a solution. Then, we study the impulse approximate controllability where the control function acts on a subdomain ω and at one instant of time τ ∈ (0, T ). Afterward, we study impulse observability.

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Background: Mediterranean shrub species cover more than 70% of the total area in Tunisia and in summer when the herbaceous species have wilted, they constitute feeding resource for livestock. The use of tanniniferous shrubs seems to be a good alternative to control gastrointestinal nematodes infections in small ruminants. This study evaluated the in vitro anthelmintic (AH) effect of Ceratonia siliqua (C. siliqua), Periploca angustifolia Labill. (P. angustifolia) and Medicago arborea (M. arborea) against Haemonchus contortus third stage larvae (L3). Methods: The larval exsheathment assay (LEA) was used to determine the proportions (%) of exsheathment of five acetonic extracts at different concentrations (1200, 600, 300, 150 μg/ml). To confirm the role of tannins in the AH effects of extracts, polyvinyl polypyrolidone (PVPP) was used as deactivating chemical tannins. Result: The highest % L3 exsheathed was recorded for M. arborea (55.01%) and the lowest value was founded for C. siliqua and P. angustifolia leaves (16.26%). Our results were concentration-dependent (P less than 0.001). The % of exsheathment increased as the time of incubation increased (P less than 0.001). P. angustifolia pods recorded the lowest EC50 value (P less than 0.05). After PVPP addition, all the acetonic extracts showed a restoration of L3 exsheathment values similar to control values (P less than 0.001).

Gastrointestinal nematodes are compromising productivity of grazing sheep and goats. Therefore, scientists have been looking for cost-effective alternative options. Forage legumes (Fabacea Family) contain tannins that could improve livestock performance and their health as well. The present study aimed to (i) determine the in vitro anthelmintic (AH) activity of 19 acetonic extracts of Hedysarum carnosum Desf on Haemonchus contortus by a larval exsheathment assay (LEA); (ii) test the anthelmintic activity of condensed tannins using a deactivating reagent, polyvinylpolypyrrolidone (PVPP); (iii) study the effect of location and the phenological stage on the percentage of exsheathment. The LEA was used at different concentrations (150, 300, 600, 1200 µg mL-1 of acetonic extract/mL of purified buffer solution (PBS)). The larval exsheathment is concentration, location, phenological stage dependent. All extracts, caused a delay of the percentage of exsheathment over 50% so the AH activity of H. carnosum was confirmed. After addition of PVPP, the % exsheathment was similar to the 150 µg mL-1 concentration. The biplot showed that Loc1(S), Loc4(B), Loc 5(PF), Loc 6(BM) and Loc 6(PF) were isolated from other plant extract sample. Our in vitro study showed that H. carnosum seems to be a promising alternative to AH drugs.