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Existence of classical solutions and feedback stabilization for the flow in gas networks

Martin Gugat, Michaël Herty (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the flow of gas through pipelines controlled by a compressor station. Under a subsonic flow assumption we prove the existence of classical solutions for a given finite time interval. The existence result is used to construct Riemannian feedback laws and to prove a stabilization result for a coupled system of gas pipes with a compressor station. We introduce a Lyapunov function and prove exponential decay with respect to the L2-norm.

Existence of classical solutions and feedback stabilization for the flow in gas networks

Martin Gugat, Michaël Herty (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the flow of gas through pipelines controlled by a compressor station. Under a subsonic flow assumption we prove the existence of classical solutions for a given finite time interval. The existence result is used to construct Riemannian feedback laws and to prove a stabilization result for a coupled system of gas pipes with a compressor station. We introduce a Lyapunov function and prove exponential decay with respect to the L2-norm.

Existence of classical solutions for parabolic functional differential equations with initial boundary conditions of Robin type

Milena Matusik (2012)

Annales Polonici Mathematici

The paper deals with the initial boundary value problem of Robin type for parabolic functional differential equations. The unknown function is the functional variable in the equation and the partial derivatives appear in the classical sense. A theorem on the existence of a classical solution is proved. Our formulation and results cover differential equations with deviated variables and differential integral problems.

Existence of entropy solutions for degenerate quasilinear elliptic equations in L 1

Albo Carlos Cavalheiro (2014)

Communications in Mathematics

In this article, we prove the existence of entropy solutions for the Dirichlet problem ( P ) - div [ ω ( x ) 𝒜 ( x , u , ∇ u ) ] = f ( x ) - div ( G ) , in Ω u ( x ) = 0 , on ∂ Ω where Ω is a bounded open set of N , N ≥ 2 , f ∈ L 1 ( Ω ) and G / ω ∈ [ L p ' ( Ω , ω ) ] N .

Existence of entropy solutions to nonlinear degenerate parabolic problems with variable exponent and L 1 -data

Abdelali Sabri, Ahmed Jamea, Hamad Talibi Alaoui (2020)

Communications in Mathematics

In the present paper, we prove existence results of entropy solutions to a class of nonlinear degenerate parabolic p ( · ) -Laplacian problem with Dirichlet-type boundary conditions and L 1 data. The main tool used here is the Rothe method combined with the theory of variable exponent Sobolev spaces.

Existence of extremal periodic solutions for nonlinear evolution inclusions

Nikolaos S. Papageorgiou, Nikolaos Yannakakis (2001)

Archivum Mathematicum

We consider a nonlinear evolution inclusion defined in the abstract framework of an evolution triple of spaces and we look for extremal periodic solutions. The nonlinear operator is only pseudomonotone coercive. Our approach is based on techniques of multivalued analysis and on the theory of operators of monotone-type. An example of a parabolic distributed parameter system is also presented.

Currently displaying 881 – 900 of 1309