Examinando por Autor "Latorre, Marta"

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Blow-up patterns for a reaction-diffusion equation with weighted reaction in general dimension
(2024) Iagar, Razvan Gabriel; Latorre, Marta; Sánchez, Ariel
We classify all the blow-up solutions in self-similar form to the following reaction-diffusion equation \partial_t u=\Delta u^m+|x|^{sigma}u^p, with m>1, 1<= p0.
Elliptic 1-Laplacian equations with dynamical boundary conditions
(2018) Latorre, Marta; Segura de León, Sergio
This paper is concerned with an evolution problem having an elliptic equation involving the 1-Laplacian operator and a dynamical boundary condition. We apply nonlinear semigroup theory to obtain existence and uniqueness results as well as a comparison principle. Our main theorem shows that the solution we found is actually a strong solution. We also compare solutions with different data.
Elliptic equations involving the 1-Laplacian and a total variation term with L^{N,\infty}-data
(2017) Latorre, Marta; Segura de León, Sergio
In this paper we study, in an open bounded set with Lipschitz boundary, the Dirichlet problem for a nonlinear singular elliptic equation involving the 1--Laplacian and a total variation term, that is, the inhomogeneous case of the equation appearing in the level set formulation of the inverse mean curvature flow. Our aim is twofold. On the one hand, we consider data belonging to the Marcinkiewicz space with a critical exponent, which leads to unbounded solutions. So, we have to begin introducing the suitable notion of unbounded solution to this problem. Moreover, examples of explicit solutions are shown. On the other hand, this equation allows us to deal with many related problems having a different gradient term which depend on a function g. It is known that the total variation term induces a regularizing effect on existence, uniqueness and regularity. We focus on analyzing whether those features remain true when general gradient terms are taken. Roughly speaking, the bigger g, the better the properties of the solution.
Eternal solutions in exponential self-similar form for a quasilinear reaction-diffusion equation with critical singular potential
(2024) Iagar, Razvan Gabriel; Latorre, Marta; Sánchez, Ariel
We prove existence and uniqueness of self-similar solutions with exponential form u(x,t)=e^{alpha t}f(|x|e^{-beta t}), alpha, beta>0, to the quasilinear reaction-diffusion equation \partial_t u=Delta u^m+|x|^{sigma}u^p, with m>1, 10 if u_0 is compactly supported.
Existence and comparison results for an elliptic equation involving the 1-Laplacian and L^1-data
(2018) Latorre, Marta; Segura de León, Sergio
This paper is devoted to analyse the Dirichlet problem for a nonlinear elliptic equation involving the 1-Laplacian and a total variation term, that is, the inhomogeneous case of the equation arising in the level set formulation of the inverse mean curvature flow. We study this problem in an open bounded set with Lipschitz boundary. We prove an existence result and a comparison principle for non-negative L^1-data. Moreover, we search the summability that the solution reaches when more regular L^p-data, with 1
Existence and uniqueness for the inhomogeneous 1-Laplace evolution equation revisited
(2022) Latorre, Marta; Segura de León, Sergio
In this paper we deal with an inhomogeneous parabolic Dirichlet problem involving the 1-Laplacian operator. We show the existence of a unique solution when data belong to L^1(0,T;L^2(\Omega)) for every T>0. As a consequence, global existence and uniqueness for data in L^1_{loc}(0,+\infty;L^2(\Omega)) is obtained. Our analysis retrieves previous results in a correct and complete way.
On classical orthogonal polynomials and the Cholesky factorization of a class of Hankel matrices
(World Scientific, 2023-04-11) Marriaga, Misael E.; Vera de Salas, Guillermo; Latorre, Marta; Muñóz Alcázar, Rubén
Classical moment functionals (Hermite, Laguerre, Jacobi, Bessel) can be characterized as those linear functionals whose moments satisfy a second-order linear recurrence relation. In this work, we use this characterization to link the theory of classical orthogonal polynomials and the study of Hankel matrices whose entries satisfy a second-order linear recurrence relation. Using the recurrent character of the entries of such Hankel matrices, we give several characterizations of the triangular and diagonal matrices involved in their Cholesky factorization and connect them with a corresponding characterization of classical orthogonal polynomials.
Optimal existence, uniqueness and blow-up for a quasilinear diffusion equation with spatially inhomogeneous reaction
(2024) Iagar, Razvan Gabriel; Latorre, Marta; Sánchez, Ariel
Well-posedness and a number of qualitative properties for solutions to the Cauchy problem for the following nonlinear diffusion equation with a spatially inhomogeneous source partial_t u=Delta u^m+|x|^{sigma}u^p, with exponents 10, are established. More precisely, we identify the optimal class of initial conditions u_0 for which (local in time) existence is ensured and prove non-existence of solutions for the complementary set of data. We establish then (local in time) uniqueness and a comparison principle for this class of data. We furthermore prove that any non-trivial solution to the Cauchy problem blows up in a finite time T and finite speed of propagation holds true for t0, then u(t) is compactly supported for t
Regularizing effects concerning elliptic equations with a superlinear gradient term
(2021) Latorre, Marta; Magliocca, Martina; Segura de León, Sergio
We consider the homogeneous Dirichlet problem for an elliptic equation driven by a linear operator with discontinuous coefficients and having a subquadratic gradient term. This gradient term behaves as g(u)|\nabla u|^q, where 1
The Dirichlet problem for the 1-Laplacian with a general singular term and L^1-data
(2021) Latorre, Marta; Oliva, Francescantonio; Petitta, Francesco; Segura de León, Sergio
We study the Dirichlet problem for an elliptic equation involving the 1-Laplace operator and a reaction term, -\Delta_1 u =h(u)f(x), where f is nonnegative and h is a continuous real function that may possibly blow up at zero. We investigate optimal ranges for the data in order to obtain existence, nonexistence and (whenever expected) uniqueness of nonnegative solutions.