All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 14 Next

Displaying 261 – 280 of 333

Showing per page

Some new error estimates for finite element methods for second order hyperbolic equations using the Newmark method

Abdallah Bradji, Jürgen Fuhrmann (2014)

Mathematica Bohemica

We consider a family of conforming finite element schemes with piecewise polynomial space of degree k in space for solving the wave equation, as a model for second order hyperbolic equations. The discretization in time is performed using the Newmark method. A new a priori estimate is proved. Thanks to this new a priori estimate, it is proved that the convergence order of the error is h k + τ 2 in the discrete norms of ℒ ∞ ( 0 , T ; ℋ 1 ( Ω ) ) and 𝒲 1 , ∞ ( 0 , T ; ℒ 2 ( Ω ) ) , where h and τ are the mesh size of the spatial and temporal discretization, respectively....

Stabilization of wave systems with input delay in the boundary control

Gen Qi Xu, Siu Pang Yung, Leong Kwan Li (2006)

ESAIM: Control, Optimisation and Calculus of Variations

In the present paper, we consider a wave system that is fixed at one end and a boundary control input possessing a partial time delay of weight ( 1 - μ ) is applied over the other end. Using a simple boundary velocity feedback law, we show that the closed loop system generates a C0 group of linear operators. After a spectral analysis, we show that the closed loop system is a Riesz one, that is, there is a sequence of eigenvectors and generalized eigenvectors that forms a Riesz basis for the state Hilbert...

Sufficient optimality conditions for multivariable control problems

Andrzej Nowakowski (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We study optimal control problems for partial differential equations (focusing on the multidimensional differential equation) with control functions in the Dirichlet boundary conditions under pointwise control (and we admit state - by assuming weak hypotheses) constraints.

The existence of Carathéodory solutions of hyperbolic functional differential equations

Adrian Karpowicz (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We consider the following Darboux problem for the functional differential equation ∂ ² u / ∂ x ∂ y ( x , y ) = f ( x , y , u ( x , y ) , ∂ u / ∂ x ( x , y ) , ∂ u / ∂ y ( x , y ) ) a.e. in [0,a]×[0,b], u(x,y) = ψ(x,y) on [-a₀,a]×[-b₀,b] 0 , a ] × ( 0 , b ] , where the function u ( x , y ) : [ - a ₀ , 0 ] × [ - b ₀ , 0 ] → ℝ k is defined by u ( x , y ) ( s , t ) = u ( s + x , t + y ) for (s,t) ∈ [-a₀,0]×[-b₀,0]. We prove a theorem on existence of the Carathéodory solutions of the above problem.

Currently displaying 261 – 280 of 333