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This paper is devoted to the design and analysis of a numerical algorithm for approximating solutions of a degenerate cross-diffusion system, which models particular instances of taxis-type migration processes under local sensing…

Numerical Analysis · Mathematics 2025-10-09 Juan Vicente Gutiérrez-Santacreu

We prove the existence of weak solutions in the space of energy for a class of non-linear Schroedinger equations in the presence of a external rough magnetic potential. Under our assumptions it is not possible to study the problem by means…

Analysis of PDEs · Mathematics 2018-04-18 Paolo Antonelli , Alessandro Michelangeli , Raffaele Scandone

Using a modified WKB approach, we present a rigorous semi-classical analysis for solutions of nonlinear Schroedinger equations with rotational forcing. This yields a rigorous justification for the hydrodynamical system of rotating…

Analysis of PDEs · Mathematics 2010-09-03 Hailiang Liu , Christof Sparber

We investigate a semilinear wave equation with energy-critical nonlinearity and a nonlinear damping mechanism driven by the total energy of the system. The model combines the quintic defocusing term with a time-dependent dissipation of the…

Analysis of PDEs · Mathematics 2026-04-06 Marcelo Cavalcanti , Valéria Domingos Cavalcanti , Josiane Faria , Cintya Okawa

We consider degenerate porous medium equations with a divergence type of drift terms. We establish the existence of $L^{q}$-weak solutions (satisfying energy estimates or even further with moment and speed estimates in Wasserstein spaces),…

Analysis of PDEs · Mathematics 2023-03-07 Sukjung Hwang , Kyungkeun Kang , Haw Kil Kim

Beginning from the semiclassical Hamiltonian, the Fermi pressure and Bohm potential for the quantum hydrodynamics application (QHD) at finite temperature are consistently derived in the framework of the local density approximation with the…

Plasma Physics · Physics 2018-04-18 Zh. A. Moldabekov , M. Bonitz , T. S. Ramazanov

Thermodynamically consistent models for two-phase flow in porous media have attracted significant attention in recent years. In this paper, we prove the existence, uniqueness and regularity of the weak solution to such a recent model…

Analysis of PDEs · Mathematics 2026-02-05 Huangxin Chen , Jisheng Kou , Haitao Leng , Shuyu Sun , Hai Zhao

We consider weak solutions to a two-dimensional simplified Ericksen-Leslie system of compressible flow of nematic liquid crystals. An initial-boundary value problem is first studied in a bounded domain. By developing new techniques and…

Analysis of PDEs · Mathematics 2013-08-13 Fei Jiang , Song Jiang , Dehua Wang

This article proposes a review of the analysis of the system of magnetohydrodynamics (MHD). First, we give an account of the modelling asumptions. Then, the results of existence of weak solutions, using the notion of renormalized solutions.…

Analysis of PDEs · Mathematics 2015-09-21 Xavier Blanc , Bernard Ducomet

In this paper we show existence of finite energy solutions for the Cauchy problem associated with a semilinear wave equation with interior damping and supercritical source terms. The main contribution consists in dealing with…

Analysis of PDEs · Mathematics 2008-11-14 Lorena Bociu , Petronela Radu

This paper studies global existence, hydrodynamic limit, and large-time behavior of weak solutions to a kinetic flocking model coupled to the incompressible Navier-Stokes equations. The model describes the motion of particles immersed in a…

Analysis of PDEs · Mathematics 2013-11-25 J. A. Carrillo , Y. -P. Choi , T. K. Karper

We prove existence of weak solutions to the obstacle problem for semilinear wave equations (including the fractional case) by using a suitable approximating scheme in the spirit of minimizing movements. This extends the results in [9],…

Analysis of PDEs · Mathematics 2021-04-05 Mauro Bonafini , Van Phu Cuong Le , Matteo Novaga , Giandomenico Orlandi

We prove the global existence of finite energy weak solutions to the general liquid crystals system. The problem is studied in bounded domain of $R^3$ with Dirichlet boundary conditions and the whole space $R^3$.

Analysis of PDEs · Mathematics 2013-05-30 Yu-ming Chu , Yi-hang Hao , Xian-gao Liu

In this paper we prove the existence of global weak dissipative martingale solutions for a one-dimensional compressible fluid model with capillarity and density dependent viscosity, driven by random initial data and a stochastic forcing…

Analysis of PDEs · Mathematics 2024-12-17 Donatella Donatelli , Lorenzo Pescatore , Stefano Spirito

We discuss a notion of weak solution for a semilinear wave equation that models the interaction of an elastic body with a rigid substrate through an adhesive layer, relying on results in [2]. Our analysis embraces the vector-valued case in…

Analysis of PDEs · Mathematics 2022-03-23 Mauro Bonafini , Van Phu Cuong Le

Concentrating on zero temperature Quantum Monte Carlo calculations of electronic systems, we give a general description of the theory of finite size extrapolations of energies to the thermodynamic limit based on one and two-body correlation…

We consider a dissipative quantum fluid on the whole space $\mathbb{R}^d$ ($d\geq 1$) confined by an external harmonic potential. The dynamics of the quantum fluid is described by the Quantum Navier-Stokes (QNS) system which is a particular…

Analysis of PDEs · Mathematics 2025-09-24 Jérémy Faupin , Ingrid Lacroix-Violet , Julien Lequeurre

This article establishes the global existence of weak solutions to a model proposed by Rosensweig (Rosensweig, Ferrohydrodynamics (1985)) for the dynamics of ferrofluids. The system is expressed by the conservation of linear momentum, the…

Analysis of PDEs · Mathematics 2019-10-02 Ricardo H. Nochetto , Konstantina Trivisa , Franziska Weber

We explore local existence and properties of classical weak solutions to the initial-boundary value problem of a one-dimensional quasilinear equation of elastodynamics with non-convex stored-energy function, a model of phase transitions in…

Analysis of PDEs · Mathematics 2016-01-26 Seonghak Kim , Youngwoo Koh

We analyze the problem for viscous incompressible heat-conduc\-ting fluid in a finite cylinder with large inflow and outflow, modelled with Navier-Stokes equations coupled with the heat equation. We prove energy estimate without…

Analysis of PDEs · Mathematics 2025-06-30 Joanna Rencławowicz , Wojciech M. Zajączkowski