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Chapter
A Degenerate Operator in Non Divergence Form
In this paper we consider a fourth order operator in non divergence form Au := au′′′′, where a : [ ...
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Article
Null Controllability for a Degenerate Population Equation with Memory
In this paper we consider the null controllability for a population model depending on time, on space and on age. Moreover, the diffusion coefficient degenerate at the boundary of the space domain. The novelty...
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Article
N. Lerner: “Carleman Inequalities”
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Article
Carleman Estimates and Controllability for a Degenerate Structured Population Model
In this paper we study the null controllability property for a single population model in which the population y depends on time t, space x, age a and size ...
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Chapter
Mathematical Tools and Preliminary Results
We give some fundamental definitions and some Hardy-type inequalities with boundary or interior degeneracy. We also show the equivalence between null controllability and observability inequality.
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Chapter
A Singular Nondegenerate Parabolic Equation
We consider non degenerate singular parabolic problems, giving some existence or non existence results, which depend on the value of the parameter of the singular term. Null controllability results are present...
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Chapter
The Case of an Interior Degenerate/Singular Parabolic Equation
We consider parabolic problems in divergence and non divergence form with interior degeneracy and singularity given by general functions, showing well posedness and null controllability.
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Chapter
The Non Singular Case: \(\lambda =0\)
We show Carleman estimates for parabolic problems in divergence or non divergence form with degeneracy at the boundary or in the interior of the space domain. By them we obtain observability inequalities, prov...
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Chapter
The Case of a Boundary Degenerate/Singular Parabolic Equation
We consider parabolic problems in divergence form with boundary degeneracy and power singularity, showing well posedness and null controllability.
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Article
Carleman estimates for parabolic equations with interior degeneracy and Neumann boundary conditions
We consider a parabolic problem with degeneracy in the interior of the spatial domain and Neumann boundary conditions. In particular, we focus on the well-posedness of the problem and on Carleman estimates for...
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Article
Superlinear Neumann problems with the p-Laplacian plus an indefinite potential
We consider nonlinear Neumann problems driven by the p-Laplacian plus an indefinite potential and with a superlinear reaction which need not satisfy the Ambrosetti–Rabinowitz condition. First, we prove an existen...
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Article
Identification of a diffusion coefficient in strongly degenerate parabolic equations with interior degeneracy
We are concerned with the identification of the diffusion coefficient u(x) in a strongly degenerate parabolic diffusion equation. The strong degeneracy means that
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Book
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Chapter
A Control Approach for an Identification Problem Associated to a Strongly Degenerate Parabolic System with Interior Degeneracy
We study an identification problem associated with a strongly degenerate parabolic evolution equation of the type $$\displaystyle{y_{t} -\mathit{Ay} ...
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Chapter
A k-uniform Maximum Principle When 0 is an Eigenvalue
In this paper we consider linear operators of the form L+ λI between suitable functions spaces, when 0 is an eigenvalue of L with constant associated eigenfunctions.We introduce a new notion of “quasi”-uniform ma...
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Article
Controllability results for a class of one-dimensional degenerate parabolic problems in nondivergence form
We give null controllability results for some degenerate parabolic equations in non divergence form on a bounded interval. In particular, the coefficient of the second order term degenerates at the extreme poi...
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Article
Classical solutions for partial functional differential equations with nonautonomous past
We study partial functional differential equations with infinite delay where the history function is modified by a backward evolution family. Under appropriate assumptions and using semigroup techniques we pro...