Search

This work studies a haptotactic cross-diffusion system modeling oncolytic virotherapy in two-dimensional domains, accounting for interaction among uninfected and infected cancer cells, extracellular matrix and oncolytic viruses. It is rigorously proved that an associated no-flux initial-boundary value problem has a unique global classical solution which is uniformly bounded under suitable assumptions. Moreover, it is shown that a bounded solution can approach spatially constant equilibrium in the large time limit. [ABSTRACT FROM AUTHOR]

Abstract This work is concerned with a quasilinear parabolic–parabolic chemotaxis model with nonlinear signal production: u t = ∇ ⋅ ((1 + u) − α ∇ u) − ∇ ⋅ (u (1 + u) β − 1 ∇ v) + f (u) , v t = Δ v − v + u γ , with nonnegative initial data under homogeneous Neumann boundary conditions in a smooth bounded domain, where α , β ∈ R and γ > 0. The logistic type source term f (u) satisfies that either f (u) ≡ 0 or f (u) = r u − μ u k with r ∈ R , μ > 0 and k > 1. The global-in-time existence and uniform-in-time boundedness of solutions are established under specific parameters conditions, which improves the known results. [ABSTRACT FROM AUTHOR]

In this paper we obtain the following local Calderón–Zygmund estimates B ( | f | ) ∈ L l o c q ( Ω ) ⇒ B ( | ∇ u | ) ∈ L l o c q ( Ω ) for any q ≥ 1 of weak solutions for a class of quasilinear elliptic equations div ( a ( | ∇ u | ) ∇ u ) = div ( a ( | f | ) f ) in Ω , where B ( t ) = ∫ 0 t τ a ( τ ) d τ for t ≥ 0 . [ABSTRACT FROM AUTHOR]

Abstract: In this paper we obtain a new global gradient estimates in weighted Lorentz spaces for weak solutions of -Laplacian type equation with small BMO coefficients in a δ-Reifenberg flat domain. The modified Vitali covering lemma, the maximal function technique and the appropriate localization method are the main analytical tools. Our results improve the known results for such equations. [Copyright &y& Elsevier]

Abstract: Under some assumptions on the continuous function , we obtain the local regularity of solutions of the strong -Laplacian by using the integral estimates in Campanato spaces. [Copyright &y& Elsevier]

Abstract: In this paper we prove the existence and uniqueness of both renormalized solutions and entropy solutions for nonlinear parabolic equations with variable exponents and data. And moreover, we obtain the equivalence of renormalized solutions and entropy solutions. [Copyright &y& Elsevier]

Abstract: In this paper we develop a unifying method to prove the existence and uniqueness of weak solutions for the initial–boundary value problem of a non-uniformly parabolic equation. Some well-known parabolic equations are the special cases of this equation. [Copyright &y& Elsevier]

Abstract: In this paper we generalize gradient estimates in spaces to Orlicz spaces for weak solutions of second-order divergence elliptic equations with small BMO coefficients in Lipschitz domains. Our results improve the known results for such equations using the harmonic analysis method. [Copyright &y& Elsevier]

Abstract: In this paper we establish a stability result and an error estimate of weak solutions for the initial-boundary value problem of a generalized thin film equation and also obtain some higher regularity results for weak solutions. [Copyright &y& Elsevier]

Abstract: In this paper we establish the existence and uniqueness of weak solutions for the initial-boundary value problem of a fourth-order nonlinear parabolic equation. [Copyright &y& Elsevier]

In this paper we study the asymptotic behaviors of global solutions to the fully parabolic chemotaxis system: u t = ∇ ⋅ (D (u) ∇ u − S (u) ∇ v) + r u − μ u 1 + σ , v t = Δ v − v + u γ , subject to the homogeneous Neumann boundary conditions in a bounded and smooth domain Ω ⊂ R n (n ≥ 2), where parameters μ , σ , γ > 0 , r ∈ R , and the nonlinearity D , S ∈ C 2 ([ 0 , ∞)) are supposed to generalize the prototypes D (u) ≥ a 0 (u + 1) − α , 0 ≤ S (u) ≤ b 0 u (u + 1) β − 1 with a 0 , b 0 > 0 and α , β ∈ R. We first consider the case of r > 0 and provide a boundedness result under α + β + γ < 2 n , or β + γ < 1 + σ , or β + γ = 1 + σ with large μ > 0. The main result is concerned with the asymptotic stability when damping effects of logistic source are strong enough. Specifically, there is μ 0 > 0 independent of initial data, such that the bounded classical solution (u , v) satisfies (u , v) → ((r μ) 1 σ , (r μ) γ σ ) in L ∞ (Ω) exponentially under conditions of μ > μ 0 and r > 0. For the case of r < 0 , the trivial constant equilibria in the model is obtained in a priori way, that is, any bounded solution (u , v) satisfies (u , v) → (0 , 0) in L ∞ (Ω) exponentially, regardless of the size of μ > 0. [ABSTRACT FROM AUTHOR]

In the paper, we establish commutator estimates for the Dirichlet-to-Neumann map of Stokes systems in Lipschitz domains. The approach is based on Dahlberg's bilinear estimates, and the results may be regarded as an extension of [8,21] to Stokes systems. [ABSTRACT FROM AUTHOR]

In this paper we establish the existence and uniqueness of weak solutions for the initial-boundary value problem of a two-dimensional low-curvature equation, which is related to image analysis. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we generalize gradient estimates in space to Orlicz space for weak solutions of elliptic equations of p-Laplacian type with small BMO coefficients in δ-Reifenberg flat domains. Our results improve the known results for such equations using a harmonic analysis-free technique. [Copyright &y& Elsevier]

Abstract: We develop a unifying method to obtain the interior and boundary estimates for the weak solution of a nonlinear elliptic partial differential equation of p-Laplacian type with BMO coefficients in a δ-Reifenberg flat domain. Our results greatly improve the known results for such equations. [Copyright &y& Elsevier]

In this study, we devoted to investigate immune-related genes and tumor microenvironment (TME) in EC based on The Cancer Genome Atlas (TCGA) database. In total 799 up-regulated and 139 down-regulated immune-related and differentially expressed genes in EC were investigated for functional annotations and prognosis. By a conjoint Cox regression analysis, we built two risk models for OS and DFS, as well as the consistent nomograms. Immune-related pathways were revealed mostly enriched in the low-risk group. By further analyzing TME based on the risk signatures, the higher immune cell infiltration and activation, lower tumor purity and higher tumor mutational burden were found in low-risk group, which presented a better prognosis. Both the expression and immunophenoscore of immune checkpoints PD-1, CTLA4, PD-L1 and PD-L2 increased significantly in low-risk group. These findings may provide new ideas for novel biomarkers and immunotherapy targets in EC. • Our present study investigated the immune-related genes and TME in EC based on TCGA database. • We built two prognostic risk models for OS and DFS based on immune-related genes of EC patients. • The higher immune status, tumor mutational burden and immune checkpoints expression was found in the low-risk group patients. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with a class of linear equations with boundary degeneracy. According to the degenerate ratio, the equations are divided into weakly degenerate ones and strongly degenerate ones, which should be supplemented by different Dirichlet boundary value conditions. After establishing some necessary existence, nonexistence and comparison principles, we investigate the optimal Hölder continuity of weak solutions in these two cases utilizing the Harnack inequality and the Morrey theorem, respectively. [Copyright &y& Elsevier]