Results 71 to 80 of about 2,262 (104)

Analysis of weak solutions of a phase-field model for sea ice evolution

Alexandria Engineering Journal, 2023
This paper is devoted to the study of the well-posedness of an initial-boundary value problem (IVBP) for a three-dimensional two-phase system, which is a phase-field model consisting of two coupled parabolic equations and is used to describe the solid ...
Md Akram Hossain, Peicheng Zhu, Li Ma
doaj  

An inhomogeneous, $L^2$ critical, nonlinear Schrödinger equation [PDF]

Z. Anal. Anwend. 31 (2012), 283-290, 2011
An inhomogeneous nonlinear Schr\"odinger equation is considered, that is invariant under $L^2$ scaling. The sharp condition for global existence of $H^1$ solutions is established, involving the $L^2$ norm of the ground state of the stationary equation.
arxiv  

Solvability of Planar Complex Vector Fields with Homogeneous Singularities [PDF]

arXiv, 2012
In this paper we study the equation $Lu=f$, where $L$ is a $\C$-valued vector field in $\R^2$ with a homogeneous singularity. The properties of the solutions are linked to the number theoretic properties of a pair of complex numbers attached to the vector field.
arxiv  

Phase transitions in porous media. [PDF]

Nonlinear Differ Equ Appl, 2022
Gavioli C, Krejčí P.
europepmc   +1 more source

On the Cauchy problem for a general fractional porous medium equation with variable density [PDF]

arXiv, 2013
We study the well-posedness of the Cauchy problem for a fractional porous medium equation with a varying density. We establish existence of weak energy solutions; uniqueness and nonuniqueness is studied as well, according with the behavior of the density at infinity.
arxiv  

On a fractional sublinear elliptic equation with a variable coefficient [PDF]

arXiv, 2013
We study existence and uniqueness of bounded solutions to a fractional sublinear elliptic equation with a variable coefficient, in the whole space. Existence is investigated in connection to a certain fractional linear equation, whereas the proof of uniqueness relies on uniqueness of solutions to an associated fractional porous medium equation with ...
arxiv  

Infinitely many free or prescribed mass solutions for fractional Hartree equations and Pohozaev identities

Advanced Nonlinear Studies
In this paper we study the following nonlinear fractional Hartree (or Choquard-Pekar) equation (−Δ)su+μu=(Iα*F(u))F′(u) inRN, ${\left(-{\Delta}\right)}^{s}u+\mu u=\left({I}_{\alpha }{\ast}F\left(u\right)\right){F}^{\prime }\left(u\right)\quad \text{in} {\
Cingolani Silvia, Gallo Marco, Tanaka Kazunaga   +2 more
doaj   +1 more source

Sliding methods for dual fractional nonlinear divergence type parabolic equations and the Gibbons’ conjecture

Advanced Nonlinear Studies
In this paper, we consider the general dual fractional parabolic problem ∂tαu(x,t)+Lu(x,t)=f(t,u(x,t))inRn×R. ${\partial }_{t}^{\alpha }u\left(x,t\right)+\mathcal{L}u\left(x,t\right)=f\left(t,u\left(x,t\right)\right) \text{in} {\mathbb{R}}^{n}{\times ...
Guo Yahong, Ma Lingwei, Zhang Zhenqiu
doaj   +1 more source

Global in time well-posedness of a three-dimensional periodic regularized Boussinesq system

Demonstratio Mathematica
Global in time weak solution to a regularized periodic three-dimensional Boussinesq system is proved to exist in energy spaces. This solution depends continuously on the initial data. In particular, it is unique.
Almutairi Shahah
doaj   +1 more source

Uniqueness for the Schrödinger Equation on Graphs with Potential Vanishing at Infinity [PDF]

arXiv
We investigate the uniqueness, in suitable weighted $\ell^p$ spaces, of solutions to the Schr\"odinger equation with a potential, posed on infinite graphs. The potential can tend to zero at infinite with a certain rate.
arxiv