Results 21 to 30 of about 472 (45)

Semiflow selection and Markov selection theorems

, 2019
The deterministic analog of the Markov property of a time-homogeneous Markov process is the semigroup property of solutions of an autonomous differential equation.
Cardona, Jorge E., Kapitanski, Lev
core   +1 more source

Local well-posedness for the nonlinear Schr\"odinger equation in the intersection of modulation spaces $M_{p, q}^s(\mathbb{R}^d) \cap M_{\infty, 1}(\mathbb{R}^d)$

, 2019
We introduce a Littlewood-Paley characterization of modulation spaces and use it to give an alternative proof of the algebra property, somehow implicitly contained in Sugimoto (2011), of the intersection $M^s_{p,q}(\mathbb{R}^d) \cap M_{\infty, 1 ...
A Bényi, A Bényi, B Wang, E Cordero, HG Feichtinger, J Toft, L Chaichenets, LH Brandenburg, M Sugimoto, PC Kunstmann, S Guo, W Guo   +11 more
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Uniqueness and nondegeneracy of ground states for −Δu+u=(Iα⋆u2)u-\Delta u+u=\left({{\rm{I}}}_{\alpha }\star {u}^{2})u in R3{{\mathbb{R}}}^{3} when α\alpha is close to 2

Advances in Nonlinear Analysis
In this article, we study the following Choquard equation: −Δu+u=(Iα⋆u2)u,x∈R3,-\Delta u+u=\left({{\rm{I}}}_{\alpha }\star {u}^{2})u,\hspace{1.0em}x\in {{\mathbb{R}}}^{3}, where Iα{{\rm{I}}}_{\alpha } is the Riesz potential and α\alpha is sufficiently ...
Luo Huxiao, Zhang Dingliang, Xu Yating
doaj   +1 more source

Well-posedness of time-fractional, advection-diffusion-reaction equations

, 2019
We establish the well-posedness of an initial-boundary value problem for a general class of time-fractional, advection-diffusion-reaction equations, allowing space- and time-dependent coefficients as well as initial data that may have low regularity. Our
Ali, Raed, Knio, Omar, McLean, William, Mustapha, Kassem   +3 more
core   +1 more source

Diffuse-interface approximation and weak–strong uniqueness of anisotropic mean curvature flow

European Journal of Applied Mathematics
The purpose of this paper is to derive anisotropic mean curvature flow as the limit of the anisotropic Allen–Cahn equation. We rely on distributional solution concepts for both the diffuse and sharp interface models and prove convergence using relative ...
Tim Laux, Kerrek Stinson, Clemens Ullrich   +2 more
doaj   +1 more source

Long time decay of incompressible convective Brinkman-Forchheimer in L2(ℝ3)

Demonstratio Mathematica
In this article, we study the global existence, uniqueness, and continuity for the solution of incompressible convective Brinkman-Forchheimer on the whole space R3{{\mathbb{R}}}^{3} when 4μβ≥14\mu \beta \ge 1.
Jlali Lotfi, Benameur Jamel
doaj   +1 more source

Dynamical behaviour of a logarithmically sensitive chemotaxis model under time-dependent boundary conditions

European Journal of Applied Mathematics
This article studies the dynamical behaviour of classical solutions of a hyperbolic system of balance laws, derived from a chemotaxis model with logarithmic sensitivity, with time-dependent boundary conditions. It is shown that under suitable assumptions
Padi Fuster Aguilera, Kun Zhao
doaj   +1 more source

Local and global existence for the Lagrangian Averaged Navier-Stokes equations in Besov spaces

, 2011
We prove the existence of short time solutions to the incompressible, isotropic Lagrangian Averaged Navier-Stokes equation with low regularity initial data in Besov spaces $B^{r}_{p,q}(\mathbb{R}^n)$, $r>n/2p$.
Pennington, Nathan
core   +1 more source

The violation of a uniqueness theorem and an invariant in the application of Poincar\'{e}--Perron theorem to Heun's equation

, 2019
The domain of convergence of a Heun function obtained through the Poincar\'{e}--Perron (P--P) theorem is not absolute convergence but conditional one [2].
Choun, Yoon-Seok
core  

Numerical investigations of non-uniqueness for the Navier-Stokes initial value problem in borderline spaces

, 2017
We consider the Cauchy problem for the incompressible Navier-Stokes equations in $\mathbb{R}^3$ for a one-parameter family of explicit scale-invariant axi-symmetric initial data, which is smooth away from the origin and invariant under the reflection ...
Guillod, Julien, Šverák, Vladimír
core