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Remarks on the control of two-phase Stefan free-boundary problems
(SIAM, 2022-10-11)
This paper concerns the null controllability of the two-phase 1D Stefan problemwith distributed controls. This is a free-boundary problem that models solidification or meltingprocesses. In each ...
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Pullback attractors for reaction-diffusion equations in some unbounded domains with an H-1 -valued non-autonomous forcing term and without uniqueness of solutions
(2010)
The existence of a pullback attractor for a reaction-diffusion equations in an unbounded domain containing a non-autonomous forcing term taking values in the space H−1, and with a continuous nonlinearity which does not ...
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Long time behavior of fractional impulsive stochastic differential equations with infinite delay
(American Institute of Mathematical Sciences, 2019-06)
This paper is first devoted to the local and global existence of mild solutions for a class of fractional impulsive stochastic differential equations with infinite delay driven by both K-valued Q-cylindrical Brownian motion ...
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Boundary controllability of parabolic coupled equations
(Elsevier, 2010-10-01)
This paper is concerned with the boundary controllability of non-scalar linear parabolic systems. More precisely, two coupled one-dimensional parabolic equations are considered. We show that, in this framework, boundary ...
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Some remarks on the comparison principle in Kirchhoff equations
(European Mathematical Society, 2018)
In this paper we study the validity of the comparison principle and the sub-supersolution method for Kirchhoff type equations. We show that these principles do not work when the Kirchhoff function is increasing, contradicting ...
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Reaction-Diffusion Equations with Non-Autonomous Force In H-1 and Delays Under Measurability Conditions on The Driving Delay Term
(Elsevier, 2014)
In this paper we analyze the existence of solutions for a reaction–diffusion problem with hereditary effects and a time-dependent force term with values in H−1. The main novelty is that the delay term may be driven by a ...
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Partial stability analysis of stochastic differential equations with a general decay rate
(Springer, 2021-08-28)
This paper is concerned with the almost sure partial practical stability of stochastic differential equations with general decay rate. We establish some sufficient conditions based upon the construction of appropriate ...
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A local result on insensitizing controls for a semilinear heat equation with nonlinear boundary Fourier conditions
(Society for Industrial and Applied Mathematics, 2004)
In this paper we present a local result on the existence of insensitizing controls for a semilinear heat equation when nonlinear boundary conditions of the form ∂ny + f(y)=0 are considered. The problem leads to an analysis ...
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Global attractor for a non-autonomous integro-differential equation in materials with memory
(2010)
The long-time behavior of an integro-differential parabolic equation of diffusion type with memory terms, expressed by convolution integrals involving infinite delays and by a forcing term with bounded delay, is investigated ...
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Analysis of a two-phase field model for the solidification of an alloy
(ScienceDirect, 2009-03-09)
In this paper we present some theoretical results for a system of nonlinear partial differential equations that provide a phase field model for the solidification/melting of a metallic alloy. It is assumed that two different ...