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Fundamental solutions to the fractional heat conduction equation in a ball under Robin boundary condition

Yuriy Povstenko (2014)

Open Mathematics

The central symmetric time-fractional heat conduction equation with Caputo derivative of order 0 < α ≤ 2 is considered in a ball under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of values of temperature and values of its normal derivative at the boundary, and the physical condition with the prescribed linear combination of values of temperature and values of the heat flux at the boundary, which is a consequence of Newton’s law of convective...

Funzioni ( p , q ) -convesse

Ennio De Giorgi, Antonio Marino, Mario Tosques (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We study a class of functions which differ essentially from those which are the sum of a convex function and a regular one and which have interesting properties related to Γ -convergence and to problems with non-convex constraints. In particular some results are given for the associated evolution equations.

Further properties of Stepanov--Orlicz almost periodic functions

Yousra Djabri, Fazia Bedouhene, Fatiha Boulahia (2020)

Commentationes Mathematicae Universitatis Carolinae

We revisit the concept of Stepanov--Orlicz almost periodic functions introduced by Hillmann in terms of Bochner transform. Some structural properties of these functions are investigated. A particular attention is paid to the Nemytskii operator between spaces of Stepanov--Orlicz almost periodic functions. Finally, we establish an existence and uniqueness result of Bohr almost periodic mild solution to a class of semilinear evolution equations with Stepanov--Orlicz almost periodic forcing term.

Further pseudodifferential operators generating Feller semigroups and Dirichlet forms.

Niels Jacob (1993)

Revista Matemática Iberoamericana

We prove for a large class of symmetric pseudo differential operators that they generate a Feller semigroup and therefore a Dirichlet form. Our construction uses the Yoshida-Hille-Ray Theorem and a priori estimates in anisotropic Sobolev spaces. Using these a priori estimates it is possible to obtain further information about the stochastic process associated with the Dirichlet form under consideration.

Further results on sliding manifold design and observation for a heat equation

Enrique Barbieri, Sergey Drakunov, J. Fernando Figueroa (2000)

Kybernetika

This article presents new extensions regarding a nonlinear control design framework that is suitable for a class of distributed parameter systems with uncertainties (DPS). The control objective is first formulated as a function of the distributed system state. Then, a control is sought such that the set in the state space where this relation is true forms an integral manifold reachable in finite time. The manifold is called a Sliding Manifold. The Sliding Mode controller implements a theoretically...

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