Results 11 to 20 of about 169 (82)
The Weak Galerkin Method for Elliptic Eigenvalue Problems
Communications in Computational Physics, 2019 This article is devoted to studying the application of the weak Galerkin (WG) finite element method to the elliptic eigenvalue problem with an emphasis on obtaining lower bounds.
Q. Zhai
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A mixed problem with only integral boundary conditions for a hyperbolic equation
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 24, Page 1279-1291, 2004., 2004 We investigate an initial boundary value problem for a second‐order hyperbolic equation with only integral conditions. We show the existence, uniqueness, and continuous dependence of a strongly generalized solution. The proof is based on an energy inequality established in a nonclassical function space, and on the density of the range of the operator ...
Abdelfatah Bouziani
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A weighted W2,p-a priori bound for a class of elliptic operators
Journal of Inequalities and Applications, 2013 We prove a weighted W2,p-a priori bound, p>1, for a class of uniformly elliptic second-order differential operators on unbounded domains. We deduce a uniqueness and existence result for the solution of the related Dirichlet problem.MSC: 35J25, 35B45 ...
S. Monsurrò, M. Transirico
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Quasilinear elliptic equations with critical potentials
Advances in Nonlinear Analysis, 2017 We study Liouville theorems for problems of the ...
D’Ambrosio Lorenzo, Mitidieri Enzo
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On a class of nonlinear reaction‐diffusion systems with nonlocal boundary conditions
Abstract and Applied Analysis, Volume 2004, Issue 9, Page 793-813, 2004., 2004 We prove the existence, uniqueness, and continuous dependence of a generalized solution of a nonlinear reaction‐diffusion system with only integral terms in the boundaries. We first solve a particular case of the problem by using the energy‐integral method. Next, via an iteration procedure, we derive the obtained results to study the solvability of the
Abdelfatah Bouziani
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Forum of Mathematics, Sigma, 2021 We establish new Strichartz estimates for orthonormal families of initial data in the case of the wave, Klein–Gordon and fractional Schrödinger equations.
Neal Bez, Sanghyuk Lee, Shohei Nakamura
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Unconditional uniqueness for the energy-critical nonlinear Schrödinger equation on $\mathbb {T}^{4}$
Forum of Mathematics, Pi, 2022 We consider the $\mathbb {T}^{4}$ cubic nonlinear Schrödinger equation (NLS), which is energy-critical. We study the unconditional uniqueness of solutions to the NLS via the cubic Gross–Pitaevskii hierarchy, an uncommon method for NLS analysis which is ...
Xuwen Chen, Justin Holmer
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Abstract and Applied Analysis, Volume 2003, Issue 10, Page 573-589, 2003., 2003 This paper deals with weak solution in weighted Sobolev spaces, of three‐point boundary value problems which combine Dirichlet and integral conditions, for linear and quasilinear parabolic equations in a domain with curved lateral boundaries. We, firstly, prove the existence, uniqueness, and continuous dependence of the solution for the linear equation.
Abdelfatah Bouziani
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Abstract and Applied Analysis, Volume 2003, Issue 16, Page 899-922, 2003., 2003 This paper deals with an initial boundary value problem with an integral condition for the two‐dimensional diffusion equation. Thanks to an appropriate transformation, the study of the given problem is reduced to that of a one‐dimensional problem. Existence, uniqueness, and continuous dependence upon data of a weak solution of this latter are proved by
Nabil Merazga, Abdelfatah Bouziani
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The Weak Galerkin Method for Linear Hyperbolic Equation
, 2018 The linear hyperbolic equation is of great interest in many branches of physics and industry. In this paper, we use the weak Galerkin method to solve the linear hyperbolic equation.
Q. Zhai +3 more
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