Search

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]

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 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 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]