Constructing eigenfunctions of strongly coupled parabolic boundary value systems

Parabolic Systems with Coupled Boundary Conditions

We consider elliptic operators with operator-valued coefficients and discuss the associated parabolic problems. The unknowns are functions with values in a Hilbert space W . The system is equipped with a general class of coupled boundary conditions of the form f|∂Ω ∈ Y and ∂f ∂ν ∈ Y⊥, where Y is a closed subspace of L(∂Ω;W ). We discuss well-posedness and further qualitative properties, systema...

Boundary optimal control of coupled parabolic PDE-ODE systems

This paper deals with boundary optimal control problem for coupled parabolic PDEODE systems. The problem is studied using infinite-dimensional state space representation of the coupled PDE-ODE system. Linearization of the non-linear system is established around a steady state profile. Using some state transformations, the linearized system is formulated as a well-posed infinite-dimensional syst...

Positive Solutions for Systems of Coupled Fractional Boundary Value Problems

We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with coupled integral boundary conditions which contain some positive constants.

Degenerate Parabolic Initial-Boundary Value Problems*

in Hilbert space and their realizations in function spaces as initial-boundary value problems for partial differential equations which may contain degenerate or singular coefficients. The Cauchy problem consists of solving (1.1) subject to the initial condition Jdu(0) = h. We are concerned with the case where the solution is given by an analytic semigroup; it is this sense in which the Canchy p...

Initial - Boundary Value Problems for Parabolic Equations