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Article
A class of moving boundary problems with a source term: application of a reciprocal transformation
We consider a new Stefan-type problem for the classical heat equation with a latent heat and phase-change temperature depending of the variable time. We prove the equivalence of this Stefan problem with a clas...
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Article
Non-invasive study to determine changes in physical properties of multilayer materials
Exposure to different types of sources, such as electrical or thermal, can cause changes in the structure of materials, for example, cracks, stresses, oxidation, corrosion, among others. The goal of this work ...
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Article
Exact solution for non-classical one-phase Stefan problem with variable thermal coefficients and two different heat source terms
A one-phase Stefan problem for a semi-infinite material is studied for special functional forms of the thermal conductivity and specific heat depending on the temperature of the phase-change material. Using th...
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Article
A class of elliptic mixed boundary value problems with (p, q)-Laplacian: existence, comparison and optimal control
The paper deals with two nonlinear elliptic equations with (p, q)-Laplacian and the Dirichlet–Neumann–Dirichlet (DND) boundary conditions, and Dirichlet–Neumann–Neumann (DNN) boundary conditions, respectively. Un...
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Article
The similarity method and explicit solutions for the fractional space one-phase Stefan problems
In this paper we obtain self-similarity solutions for a one-phase one-dimensional fractional space Stefan problem in terms of the three parametric Mittag-Leffler function
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Article
Tykhonov well-posedness of a heat transfer problem with unilateral constraints
We consider an elliptic boundary value problem with unilateral constraints and subdifferential boundary conditions. The problem describes the heat transfer in a domain D ⊂ ℝd and its weak formulation is in the fo...
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Article
Open AccessExistence, Comparison, and Convergence Results for a Class of Elliptic Hemivariational Inequalities
In this paper we study a class of elliptic boundary hemivariational inequalities which originates in the steady-state heat conduction problem with nonmonotone multivalued subdifferential boundary condition on ...
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Article
Explicit solutions for distributed, boundary and distributed-boundary elliptic optimal control problems
We consider a steady-state heat conduction problem in a multidimensional bounded domain \(\Omega \) Ω for the Poisson equation with constant internal energy g and mixed boundary conditions given by a constant...
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Article
On the Tykhonov Well-Posedness of an Antiplane Shear Problem
We consider a boundary value problem which describes the frictional antiplane shear of an elastic body. The process is static and friction is modeled with a slip-dependent version of Coulomb’s law of dry frict...
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Article
On the paper D. Burini, S De Lillo, G. Fioriti, Acta Mech., 229 No. 10 (2018), pp 4215–4228
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Article
Explicit solution for a two-phase fractional Stefan problem with a heat flux condition at the fixed face
A generalized Neumann solution for the two-phase fractional Lamé–Clapeyron–Stefan problem for a semi-infinite material with constant initial temperature and a particular heat flux condition at the fixed face i...
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Article
Similarity solution for a two-phase one-dimensional Stefan problem with a convective boundary condition and a mushy zone model
A two-phase solidification process for a one-dimensional semi-infinite material is considered. It is assumed that it is ensued from a constant bulk temperature present in the vicinity of the fixed boundary, wh...
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Article
Open AccessA family of singular ordinary differential equations of the third order with an integral boundary condition
We establish in this paper the equivalence between a Volterra integral equation of the second kind and a singular ordinary differential equation of the third order with two initial conditions and an integral b...
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Article
Exact solution for a two-phase Stefan problem with variable latent heat and a convective boundary condition at the fixed face
Recently, in Tarzia (Thermal Sci 21A:1–11, 2017) for the classical two-phase Lamé–Clapeyron–Stefan problem an equivalence between the temperature and convective boundary conditions at the fixed face under a certa...
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Article
Open AccessNon-classical heat conduction problem with nonlocal source
We consider the non-classical heat conduction equation, in the domain D ...
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Article
Determination of Two Unknown Thermal Coefficients Through an Inverse One-Phase Fractional Stefan Problem
We consider a semi-infinite one-dimensional phase-change material with two unknown constant thermal coefficients among the latent heat per unit mass, the specific heat, the mass density and the thermal conduct...
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Article
Open AccessExplicit solutions for a non-classical heat conduction problem for a semi-infinite strip with a non-uniform heat source
A non-classical initial and boundary value problem for a non-homogeneous one-dimensional heat equation for a semi-infinite material with a zero temperature boundary condition is studied. It is not a standard h...
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Article
Convergence of optimal control problems governed by second kind parabolic variational inequalities
We consider a family of optimal control problems where the control variable is given by a boundary condition of Neumann type. This family is governed by parabolic variational inequalities of the second kind. W...
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Chapter and Conference Paper
On Existence, Uniqueness, and Convergence of Optimal Control Problems Governed by Parabolic Variational Inequalities
I) We consider a system governed by a free boundary problem with Tresca condition on a part of the boundary of a material domain with a source term g through a parabolic variational inequality of the second kind....
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Article
Convergence of distributed optimal control problems governed by elliptic variational inequalities
First, let u g be the unique solution of an elliptic variational inequality with source term g. We establish, in the general case, the error estimate between ...
