Results 11 to 20 of about 1,129 (70)
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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On an elliptic equation arising from photo-acoustic imaging in inhomogeneous media [PDF]
, 2015 We study an elliptic equation with measurable coefficients arising from photo-acoustic imaging in inhomogeneous media. We establish Holder continuity of weak solutions and obtain pointwise bounds for Green's functions subject to Dirichlet or Neumann ...
Ammari, Habib +3 more
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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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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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On two-dimensional nonlocal Venttsel' problems in piecewise smooth domains [PDF]
, 2019 We establish the regularity results for solutions of nonlocal Venttsel' problems in polygonal and piecewise smooth two-dimensional ...
Creo, Simone +3 more
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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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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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Monotonicity formulas for coupled elliptic gradient systems with applications
Advances in Nonlinear Analysis, 2019 Consider the following coupled elliptic system of ...
Fazly Mostafa, Shahgholian Henrik
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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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