We prove the interior null–controllability of one–dimensional parabolic equations with time independent measurable coefficients.

Quasi-exactly solvable one-dimensional Schrödinger equations can be specified in order to exhibit supplementary analytic eigenstates. While the usual solutions are preserved by the sl(2,R) generators, the additional ones are stabilized at the level of the universal enveloping algebra of this Lie structure. We discuss the square-integrability, the orthogonality of these supplementary solutions a...

We prove existence and uniqueness of the solution of a one-dimensional rough differential equation driven by a step-2 rough path and reflected at zero. In order to deal with the lack of control of the reflection measure the proof uses some ideas we introduced in a previous work dealing with rough kinetic PDEs [arXiv:1604.00437].

We focus in this work on the numerical discretization of the one dimensional aggregation equation ∂tρ + ∂x(vρ) = 0, v = a(W ′ ∗ ρ), in the attractive case. Finite time blow up of smooth initial data occurs for potential W having a Lipschitz singularity at the origin. A numerical discretization is proposed for which the convergence towards duality solutions of the aggregation equation is proved....

In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...

In this paper, we study the existence of extremal solutions forimpulsive delay fuzzy integrodifferential equations in$n$-dimensional fuzzy vector space, by using monotone method. Weshow that obtained result is an extension of the result ofRodr'{i}guez-L'{o}pez cite{rod2} to impulsive delay fuzzyintegrodifferential equations in $n$-dimensional fuzzy vector space.

In this work, we introduce a novel method for solving two-dimensional fuzzy Fredholm integral equations of the second kind (2D-FFIE-2). We use new representation of parametric form of fuzzy numbers and convert a two-dimensional fuzzy Fredholm integral equation to system of two-dimensional Fredholm integral equations of the second kind in crisp case. We can use Adomian decomposition method for n...