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Error estimates in L∞(0,T;L2(Ω)), L∞(0,T;L2(Ω)2), L∞(0,T;L∞(Ω)), L∞(0,T;L∞(Ω)2), Ω in $ℝ^{2}$ , are derived for a mixed finite element method for the initial-boundary value problem for integro-differential equation $u_{t} = div {a ▽ u + \int_{0}^{t} b_{1} ▽ u d τ + \int_{0}^{t} 𝐜 u d τ} + f$ based on the Raviart-Thomas space Vh x Wh ⊂ H(div;Ω) x L2(Ω). Optimal order estimates are obtained for the approximation of u,ut in L∞(0,T;L2(Ω)) and the associated velocity p in L∞(0,T;L2(Ω)2), divp in L∞(0,T;L2(Ω)). Quasi-optimal order estimates are obtained for the approximation...

lnfinitely many solutions for fractional Schrödinger equations with perturbation via variational methods

Peiluan Li, Youlin Shang (2017)

Open Mathematics

Using variational methods, we investigate the solutions of a class of fractional Schrödinger equations with perturbation. The existence criteria of infinitely many solutions are established by symmetric mountain pass theorem, which extend the results in the related study. An example is also given to illustrate our results.

L∞-Norm minimal control of the wave equation: on the weakness of the bang-bang principle

Martin Gugat, Gunter Leugering (2008)

ESAIM: Control, Optimisation and Calculus of Variations

 For optimal control problems with ordinary differential equations where the $L^{\infty}$ -norm of the control is minimized, often bang-bang principles hold. For systems that are governed by a hyperbolic partial differential equation, the situation is different: even if a weak form of the bang-bang principle still holds for the wave equation, it implies no restriction on the form of the optimal control. To illustrate that for the Dirichlet boundary control of the wave equation in general not even feasible...

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List of communications presented in sections

List of communications presented in sections

List of invited addreses

List of invited speakers

List of Participants

Littlewood-Paley a priori estimates for parabolic equations with sub-Dini continuous coefficients

Littlewood-paley decomposition associated with the dunkl operators and paraproduct operators.

Ljusternik-Schnirelmann theory on $C^{1}$ -manifolds

L∞(L2) and L∞(L∞) error estimates for mixed methods for integro-differential equations of parabolic type

lnfinitely many solutions for fractional Schrödinger equations with perturbation via variational methods

L∞-Norm minimal control of the wave equation: on the weakness of the bang-bang principle

Local a posteriori estimates for the Stokes problem.

Local a priori estimates in Lp for first order linear operators with nonsmooth coefficients.

Local analyticity in the time and space variables and the smoothing effect for the fifth-order KdV-type equation.

Local and global estimates for solutions of systems involving the $p$ -Laplacian in unbounded domains.

Local and global existence and behaviour for $t \to \infty$ of solutions of the Navier-Stokes equations

Local and global integrability of gradients in obstacle problems.

Local and global nonexistence of solutions to semilinear evolution equations.

Local approximation estimators for algebraic multigrid.

Local asymptotic symmetry of singular solutions to nonlinear elliptic equations.

Currently displaying 341 – 360 of 556