Results 21 to 30 of about 1,162 (78)
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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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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Initial‐boundary value problem with a nonlocal condition for a viscosity equation
International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 6, Page 327-338, 2002., 2002 This paper deals with the proof of the existence, uniqueness, and continuous dependence of a strong solution upon the data, for an initial‐boundary value problem which combine Neumann and integral conditions for a viscosity equation. The proof is based on an energy inequality and on the density of the range of the linear operator corresponding to the ...
Abdelfatah Bouziani
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On the solvability of parabolic and hyperbolic problems with a boundary integral condition
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 4, Page 201-213, 2002., 2002 We prove the existence, uniqueness, and the continuous dependence of a generalized solution upon the data of certain parabolic and hyperbolic equations with a boundary integral condition. The proof uses a functional analysis method based on a priori estimates established in nonclassical function spaces, and on the density of the range of the linear ...
Abdelfatah Bouziani
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Calderón–Zygmund theory for parabolic obstacle problems with nonstandard growth
Advances in Nonlinear Analysis, 2014 We establish local Calderón–Zygmund estimates for solutions to certain parabolic problems with irregular obstacles and nonstandard p(x,t)${p(x,t)}$-growth.
Erhardt André
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On a class of nonclassical hyperbolic equations with nonlocal conditions
International Journal of Stochastic Analysis, Volume 15, Issue 2, Page 125-140, 2002., 2002 This paper proves the existence, uniqueness and continuous dependence of a solution of a class of nonclassical hyperbolic equations with nonlocal boundary and initial conditions. Results are obtained by using a functional analysis method based on an a priori estimate and on the density of the range of the linear operator corresponding to the abstract ...
Abdelfatah Bouziani
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Boundedness of Solutions to a Parabolic-Elliptic Keller–Segel Equation in ℝ2 with Critical Mass
Advanced Nonlinear Studies, 2018 We consider the Cauchy problem for a parabolic-elliptic system in ℝ2{\mathbb{R}^{2}}, called the parabolic-elliptic Keller–Segel equation, which appears in various fields in biology and physics.
Nagai Toshitaka, Yamada Tetsuya
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Abstract and Applied Analysis, Volume 7, Issue 10, Page 517-530, 2002., 2002 We deal with a three point boundary value problem for a class of singular parabolic equations with a weighted integral condition in place of one of standard boundary conditions. We will first establish an a priori estimate in weighted spaces. Then, we prove the existence, uniqueness, and continuous dependence of a strong solution.
Abdelfatah Bouziani
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, 2003 International Journal of Stochastic Analysis, Volume 16, Issue 1, Page 69-79, 2003.
M. Denche, A. L. Marhoune
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International Journal of Mathematics and Mathematical Sciences, Volume 26, Issue 7, Page 417-426, 2001., 2001 We study a mixed problem with integral boundary conditions for a third‐order partial differential equation of mixed type. We prove the existence and uniqueness of the solution. The proof is based on two‐sided a priori estimates and on the density of the range of the operator generated by the considered problem.
M. Denche, A. L. Marhoune
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