In this paper we prove the existence of solution for a class of degenerate hyperbolic equations defined in whole space RN. Using some integral estimates we also prove a stability result for the problem. Finally, we also prove a blow-up result when the initial data satisfies an appropriate assumption. The main operator of the equation involves the so called Grushin operator and main goal of this paper is to introduce a new set of mathematical problems in the context of stability and blow-up results.
We investigate a nonlocal elliptic boundary value problem of logistic type involving nonlocal diffusion and global cooperative–competitive interactions:{−Δu−∫ΩK(x,y)u(y)dy=a(x)u+λ|u|p−2u∫ΩQ(x,y)|u(y)|pdy+f(x),x∈Ω,u=0,x∈∂Ω, where Ω⊂RN is a bounded smooth domain, λ∈R, 1 0. In the competitive case, we establish the existence of nonnegative weak solutions via a direct minimization argument and identify a natural spectral threshold associated with the underlying nonlocal operator. In the general case λ∈R, we employ a saddle-point framework based on Ky Fan's minimax principle to obtain existence results under suitable smallness conditions on the coefficients. These results show how the nonlocal interaction term restores coercivity and provide a unified variational framework for logistic-type elliptic problems with global interactions.
This study investigated the performance of four hydrochars derived from açaí seeds and curauá mucilage for methylene blue (MB) removal from aqueous solutions. Untreated (AWR, CWR) and phosphoric acid-treated (AAR, CAR) hydrochars were produced via hydrothermal carbonization and comprehensively characterized by Boehm titration, pHpzc, FTIR, SEM, TG/DTG, surface area, and elemental analyses. A 23- factorial experimental design was employed to optimize adsorption conditions (pH, adsorbent dosage, and initial MB concentration). The statistical models explained more than 90
Neuroworsening (NW) after traumatic brain injury (TBI) is a life-threatening complication affecting at least one in five patients. The current definition remains heterogeneous and does not integrate contemporary neuromonitoring tools that could help reduce this variability. Current diagnostic approaches are predominantly reactive, identifying deterioration only after brain herniation has occurred. To establish an expert consensus to update the definition of NW in TBI by proposing a stratified diagnostic framework aligned with precision and personalized medicine principles, aiming to shift a paradigm that has been in use for the past 50 years. A formal Delphi consensus process was conducted involving 25 experts from the Latin American Brain Injury Consortium (LABIC) and the Latin American Federation of Neurosurgical Societies (FLANC). A pre-consensus systematic literature review was performed, followed by structured electronic surveys with Likert-scale and multiple-choice items. Consensus was predefined as ≥80
The Brazilian semi-arid region is composed of a landscape mosaic that reflects a complex and diversified soil cover. In this context, research that integrates geology and geomorphology can efficiently guide pedological investigations in heterogeneous environments. This research was aimed at evaluating the soil-landscape relationships and their correlation with soil attributes in a toposequence over granites in the semi-arid region (Caatinga) of Northeastern Brazil. A transect was delimited in the landscape, and in each slope segment, a soil profile was described and sampled, namely: a) summit (P1); b) shoulder (P2); (c) backslope (P3), and; footslope (P4). Physical and chemical attributes were evaluated. Mineralogical analyses of sand, silt, and clay fractions were conducted by X-ray diffraction, and the total contents of major elements were determined by X-ray fluorescence. An E horizon in the upper third confirms that argilluviation is an active process in this landscape segment. Elutriation and argillization (in situ clay formation) also form the textural gradient, including in the foothill segment, producing Lixisols with strong rubification in the Bt horizon. Expansive clays (e.g., montmorillonite) contribute to vertisolization and the higher exchangeable and total calcium and magnesium contents in the top and foothill segments (Vertisols). At the summit, the melanization of the Bw diagnostic horizon is also evident. The variation in morphological, physical, chemical, and mineralogical attributes under similar parent materials confirms the role of relief in the distribution of materials along the toposequence and in the genesis of soils.
