Sun, Guangling Xu, Lu Zhang, Ping
Published in
Acta Mathematica Scientia

In this paper, we prove the uniqueness of the Lp Minkowski problem for q-torsional rigidity with p > 1 and q > 1 in smooth case. Meanwhile, the Lp Brunn-Minkowski inequality and the Lp Hadamard variational formula for q-torsional rigidity are established.

Campos, Luccas Guzmán, Carlos M.
Published in
Zeitschrift für angewandte Mathematik und Physik

We consider the inhomogeneous nonlinear Schrödinger equation with inverse-square potential in RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^N$$\end{do...

Le, Phuong
Published in
Acta Mathematica Scientia

Let 0 0 for all s, t ≥ 0. The main technique we use is the method of moving spheres in integral forms. Since our assumptions are more general than those in the previous literature, some new ideas are introduced to overcome this difficulty.

Kirane, Mokhtar Aimene, Djihad Seba, Djamila
Published in
Zeitschrift für angewandte Mathematik und Physik

This paper is a development of the results and techniques of the two papers (Carvalho-Neto and Planas in J Differ Equ 259:2948–2980, 2015; Oka in J Math Anal Appl 473:382–407, 2019) for the aim of addressing the existence and uniqueness of local and global mild solutions, on the Heisenberg group Hd\documentclass[12pt]{minimal} \usepackage{amsmath} ...

Cobb, Dimitri

In this article, we study bounded solutions of Euler-type equations on $R^d$ which have no integrability at $|x| \rightarrow + \infty$. As has been previously noted, such solutions fail to achieve uniqueness in an initial value problem, even under strong smoothness conditions. This contrasts with well-posedness results that have been obtained by us...

Amosov, Andrey
Published in
Zeitschrift für angewandte Mathematik und Physik

We consider a stationary boundary value problem describing a radiative–conductive heat transfer in a semitransparent body with absolutely black inclusions. To describe the radiative transfer, the integro-differential radiative transfer equation is used. We do not take into account the dependence of the radiation intensity and the properties of semi...

Dong, Hongjie Gao, Yuan
Published in
Calculus of Variations and Partial Differential Equations

We study the well-posedness of the vector-field Peierls–Nabarro model for curved dislocations with a double well potential and a bi-states limit at far field. Using the Dirichlet to Neumann map, the 3D Peierls–Nabarro model is reduced to a nonlocal scalar Ginzburg–Landau equation. We derive an integral formulation of the nonlocal operator, whose ke...

Grandmont, Céline Vergnet, Fabien
Published in
Journal of Mathematical Fluid Mechanics

We consider a quasi-static fluid–structure interaction problem where the fluid is modeled by the Stokes equations and the structure is an active elastic material. More precisely, the displacement of the structure satisfies the equations of elasticity with an additional active stress, which models the presence of internal biological motors in the st...

Rege, Alexandre

We show propagation of moments in velocity for the 3-dimensional Vlasov-Poisson system with a uniform magnetic field B = (0, 0, ω) by adapting the work of Lions, Perthame. The added magnetic field also produces singularities at times which are the multiples of the cyclotron period t = 2πk ω , k ∈ N. This result also allows to show propagation of re...

Abbatiello, Anna Feireisl, Eduard
Published in
Journal of Nonlinear Science

Let S={τn}n=1∞⊂(0,T)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {S}} = \{ \tau _n \}_{n=1}^\infty \subset (0,T)$$\end{document} be an arbitrary countable ...