scholarly journals Boundary value control problems involving the bessel differential operator

1986 ◽  
Vol 27 (4) ◽  
pp. 453-472 ◽  
Author(s):  
K.-D. Werner
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Necessary Conditions ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Finite Energy ◽  
Control Problems ◽  
Hyperbolic Partial Differential Equation ◽  
Boundary Controllability ◽  
Bessel Differential Operator

AbstractIn this paper, we consider the hyperbolic partial differential equation wrr = wrr + 1/r wr − ν2 /r2w, where v ≥ 1/2 or ν = 0 is aprameter, with the Dirichlet, Neumann and mixed boundary conditions. The boundary controllability for such problems is investigated. The main resutl is that all “finite energy” intial states can be steered to the zero state in time T, using a control f ∈ L2 (0, T), provided T > 2. Furthermore, necessary conditions for controllability are also presented.

scholarly journals An observation problem for the Bessel differential operator

1984 ◽  
Vol 26 (1) ◽  
pp. 92-107 ◽  
Author(s):  
K.-D. Werner
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Parabolic Partial Differential Equation ◽  
Final State ◽  
Bessel Differential Operator ◽  
State Observability

AbstractIn this paper, the parabolic partial differential equation ut = urr + (1/r)ur − (v2/r2)u, where v ≥ 0 is a parameter, with Dirichlet, Neumann, and mixed boundary conditions is considered. The final state observability for such problems is investigated.

scholarly journals A Novel High Dimensional Fitted Scheme for Stochastic Optimal Control Problems

2021 ◽  
Author(s):  
Christelle Dleuna Nyoumbi ◽  
Antoine Tambue
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Optimal Control ◽  
Finite Difference Method ◽  
Stochastic Optimal Control ◽  
Optimal Control Problems ◽  
Hjb Equation ◽  
High Dimensional ◽  
Control Problems ◽  
Volume Method

AbstractStochastic optimal principle leads to the resolution of a partial differential equation (PDE), namely the Hamilton–Jacobi–Bellman (HJB) equation. In general, this equation cannot be solved analytically, thus numerical algorithms are the only tools to provide accurate approximations. The aims of this paper is to introduce a novel fitted finite volume method to solve high dimensional degenerated HJB equation from stochastic optimal control problems in high dimension ($$ n\ge 3$$ n ≥ 3 ). The challenge here is due to the nature of our HJB equation which is a degenerated second-order partial differential equation coupled with an optimization problem. For such problems, standard scheme such as finite difference method losses its monotonicity and therefore the convergence toward the viscosity solution may not be guarantee. We discretize the HJB equation using the fitted finite volume method, well known to tackle degenerated PDEs, while the time discretisation is performed using the Implicit Euler scheme.. We show that matrices resulting from spatial discretization and temporal discretization are M-matrices. Numerical results in finance demonstrating the accuracy of the proposed numerical method comparing to the standard finite difference method are provided.

scholarly journals Pemodelan Tsunami Sederhana dengan Menggunakan Persamaan Differensial Parsial

2018 ◽  
Vol 8 (1) ◽  
pp. 26
Author(s):  
Indriati Retno Palupi ◽  
Wiji Raharjo ◽  
Eko Wibowo ◽  
Hafiz Hamdalah
Keyword(s):  
Differential Equation ◽  
Fluid Dynamics ◽  
Partial Differential Equation ◽  
Wave Propagation ◽  
Taylor Expansion ◽  
Tsunami Wave ◽  
Time Function ◽  
Hyperbolic Partial Differential Equation ◽  
Partial Differential ◽  
Space And Time

One way to solve fluid dynamics problem is using partial differential equation. By using Taylor expansion, fluid dynamics can be applied simply. For the example is tsunami wave. It is include to hyperbolic partial differential equation, tsunami wave propagation can describe in space and time function by using Euler FTCS (Forward Time Central Space) formula.

Composition and invariance methods for solving some stochastic control problems

1975 ◽  
Vol 7 (02) ◽  
pp. 299-329 ◽  
Author(s):  
V. E. Beneš
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dynamical Systems ◽  
White Noise ◽  
Stochastic Control ◽  
Analytical Methods ◽  
Control Problems ◽  
Numerical Treatment ◽  
Partial Differential ◽  
Stochastic Control Problems

This paper considers certain stochastic control problems in which control affects the criterion through the process trajectory. Special analytical methods are developed to solve such problems for certain dynamical systems forced by white noise. It is found that some control problems hitherto approachable only through laborious numerical treatment of the non-linear Bellman-Hamilton-Jacobi partial differential equation can now be solved.

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