Results 21 to 30 of about 1,232 (95)
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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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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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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Global $L^{p}$ estimates for degenerate Ornstein-Uhlenbeck operators with variable coefficients [PDF]
, 2012 We consider a class of degenerate Ornstein-Uhlenbeck operators in $\mathbb{R}^{N}$, of the kind [\mathcal{A}\equiv\sum_{i,j=1}^{p_{0}}a_{ij}(x) \partial_{x_{i}x_{j}}^{2}+\sum_{i,j=1}^{N}b_{ij}x_{i}\partial_{x_{j}}%] where $(a_{ij})$ is symmetric ...
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Journal of Applied Mathematics, Volume 2003, Issue 10, Page 487-502, 2003., 2003 We consider a mixed problem with Dirichlet and integral conditions for a second‐order hyperbolic equation with the Bessel operator. The existence, uniqueness, and continuous dependence of a strongly generalized solution are proved. The proof is based on an a priori estimate established in weighted Sobolev spaces and on the density of the range of the ...
Abdelfatah Bouziani
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Liouville-type theorem for some nonlinear systems in a half-space
Journal of Inequalities and Applications, 2014 In this paper we consider the following Hardy-Littlewood-Sobolev (HLS)-type system of nonlinear equations in the half-space R+n: u(x)=∫R+n(1|x−y|n−α−1|x∗−y|n−α)vq(y)dy, v(x)=∫R+n(1|x−y|n−α−1|x∗−y|n−α)up(y)dy, where p,q>1 and x∗ is the reflection of x ...
Linfen Cao, Zhaohui Dai, Wenyan Li
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Maximum Principle and Its Application for the Time-Fractional Diffusion Equations [PDF]
, 2011 MSC 2010: 26A33, 33E12, 35B45, 35B50, 35K99, 45K05 Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversaryIn the paper, maximum principle for the generalized time-fractional diffusion equations including the multi-term diffusion ...
Luchko, Yury
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Generalized Cahn‐Hilliard equations based on a microforce balance
Journal of Applied Mathematics, Volume 2003, Issue 4, Page 165-185, 2003., 2003 We present some models of Cahn‐Hilliard equations based on a microforce balance proposed by M. Gurtin. We then study the existence and uniqueness of solutions.
Alain Miranville
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Boundary value problem with integral conditions for a linear third‐order equation
Journal of Applied Mathematics, Volume 2003, Issue 11, Page 553-567, 2003., 2003 We prove the existence and uniqueness of a strong solution for a linear third‐order equation with integral boundary conditions. The proof uses energy inequalities and the density of the range of the generated operator.
M. Denche, A. Memou
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