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Exponential stability conditions for non-autonomous differential equations with unbounded commutators in a Banach space
We consider the equation d y ( t )/d t = ( A + B ( t )) y ( t ) ( t ≽ 0), where A is the generator of an analytic semigroup (e At ) t ≽0 on a Banach space χ , B ( t ) is a...
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On a Lotka-Volterra Competition Diffusion Model with Advection
In this paper, the author focuses on the joint effects of diffusion and advection on the dynamics of a classical two species Lotka-Volterra...
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An optimal control problem for a Lotka-Volterra competition model with chemo-repulsion
In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain...
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Parameters Identification in a Saltwater Intrusion Problem
This article is devoted to the identification, from observations or field measurements, of the hydraulic conductivity K for the saltwater intrusion...
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Convergence of an implicit Euler Galerkin scheme for Poisson–Maxwell–Stefan systems
A fully discrete Galerkin scheme for a thermodynamically consistent transient Maxwell–Stefan system for the mass particle densities, coupled to the...
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Global well-posedness of coupled parabolic systems
The initial boundary value problem of a class of reaction-diffusion systems (coupled parabolic systems) with nonlinear coupled source terms is...
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Well-posedness and fast-diffusion limit for a bulk–surface reaction–diffusion system
We analyze a certain class of coupled bulk–surface reaction–drift–diffusion systems arising in the modeling of signalling networks in biological...
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Mathematical Analysis of a Chemotaxis-Type Model of Soil Carbon Dynamic
The goal of this paper is to study the mathematical properties of a new model of soil carbon dynamics which is a reaction-diffusion system with a...
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Gradient estimates for parabolic systems from composite material
In this paper, we derive W 1,∞ and piecewise C 1,α estimates for solutions, and their t -derivatives, of divergence form parabolic systems with...
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Global wellposedness for a class of reaction–advection–anisotropic-diffusion systems
We prove existence and uniqueness of global solutions for a class of reaction–advection– anisotropic-diffusion systems whose reaction terms have a...
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Cauchy problems for parabolic equations in Sobolev–Slobodeckii and Hölder spaces on uniformly regular Riemannian manifolds
In this paper, we establish optimal solvability results—maximal regularity theorems—for the Cauchy problem for linear parabolic differential...
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On a Caginalp phase-field system with a logarithmic nonlinearity
We consider a phase field system based on the Maxwell Cattaneo heat conduction law, with a logarithmic nonlinearity, associated with Dirichlet...
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Second order PDEs with Dirichlet white noise boundary conditions
In this paper, we study inhomogeneous Dirichlet boundary problems associated to the Poisson and heat equations on bounded and unbounded domains with...
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On a Free Boundary Problem for a Two-Species Weak Competition System
We study a Lotka–Volterra type weak competition model with a free boundary in a one-dimensional habitat. The main objective is to understand the...
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Regularity and uniqueness in quasilinear parabolic systems
Inspired by a problem in steel metallurgy, we prove the existence, regularity, uniqueness, and continuous data dependence of solutions to a coupled...