Fig 1 - uploaded by Arezki Kheloufi
Content may be subject to copyright.
Source publication
This article deals with the parabolic equation ∂tw − c(t)∂2x w = f in D, D = { (t, x) ∈ R2 : t > 0, φ1 (t) < x < φ2(t) } with φi : [0,+∞[→ R, i = 1, 2 and c : [0,+∞[→ R satisfying some conditions and the problem is supplemented with boundary conditions of Dirichlet-Robin type. We study the global regularity problem in a suitable parabolic Sobolev s...
Similar publications
![The reference macro-element K^h\documentclass[12pt]{minimal}...](publication/361654330/figure/fig1/AS:1182638014509056@1658974283119/The-reference-macro-element-Khdocumentclass12ptminimal-usepackageamsmath_Q320.jpg)
![Nodal points {yi}\documentclass[12pt]{minimal} \usepackage{amsmath}...](publication/361654330/figure/fig2/AS:1182638014496768@1658974283144/Nodal-points-yidocumentclass12ptminimal-usepackageamsmath-usepackagewasysym_Q320.jpg)
![Nodal points of P3\documentclass[12pt]{minimal} \usepackage{amsmath}...](publication/361654330/figure/fig3/AS:1182638014504960@1658974283172/Nodal-points-of-P3documentclass12ptminimal-usepackageamsmath-usepackagewasysym_Q320.jpg)
![Nodal points and moments of P5\documentclass[12pt]{minimal}...](publication/361654330/figure/fig4/AS:1182638014513162@1658974283198/Nodal-points-and-moments-of-P5documentclass12ptminimal-usepackageamsmath_Q320.jpg)
We develop a new approach to construct finite element methods to solve the Poisson equation. The idea is to use the pointwise Laplacian as a degree of freedom followed by interpolating the solution at the degree of freedom by the given right-hand side function in the partial differential equation. The finite element solution is then the Galerkin pr...
Application of common reflection surface (CRS) to velocity variation with azimuth (VVAz) inversion of the relatively narrow azimuth 3D seismic land data Abstract: The fracture direction and its intensity are critical properties related to hydrocarbon characterization and identification. Both these properties have an essential role in identifying th...
We present a semi-Lagrangian method for the numerical resolution of Vlasov-type equations on multi-patch meshes. We employ a local cubic spline interpolation with Hermite boundary conditions between the patches. The derivative reconstruction is adapted to cope with non-uniform meshes as well as non-conforming situations. In the conforming case, the...
A new 9-DOF triangular plate finite element for linear-elastic analysis of very thin to thick plates with small deformations is presented. The element is based on Mindlin plate theory and has higher-order interpolations that are conceived to satisfy all differential equations, including the equilibrium ones based on which the shear stress resultant...
A major obstacle to the application of the standard Radial Basis Function-generated Finite Difference (RBF-FD) meshless method is constituted by its inability to accurately and consistently solve boundary value problems involving Neumann boundary conditions (BCs). This is also due to ill-conditioning issues affecting the interpolation matrix when b...
Citations
This paper is devoted to the analysis of the following linear parabolic equation ?tu-?2xu = f, subject to Robin type conditions ?x u + ?u = 0, on the lateral boundary, where coefficient ? satisfies suitable non-degeneracy assumptions and possibly depends on the time variable. The right-hand side ? of the equation is taken in Lp, 1 < p < ?. The problem is set in a domain of the form ? = {(t, x) ? R2 : 0 < t < 1, 0 < x < t?}, ? > 1/2. We use Labbas-Terreni results [23] on the operator?s sum method in the non-commutative case. This work is an extension of the Hilbertian case studied in [15].
This paper addresses linear quadratic control optimal problems for non-autonomous linear control systems using strongly continuous quasi semigroups. Riccati equations are implemented to investigate the control optimal problems of cost functional with finite and infinite horizons. The unique optimal pair for the cost functional is determined by the mild solution of the associated closed-loop problem and the feedback control of the solution of the corresponding Riccati equation. In addition for the infinite horizon, the stabilizability of the system is a sufficiency for the solvability to the Riccati equation. An application in a parabolic system is proposed.
