Zobrazeno 1 - 10
of 115
pro vyhledávání: '"Knopf Patrik"'
Publikováno v:
Advances in Nonlinear Analysis, Vol 11, Iss 1, Pp 159-197 (2021)
A cost function involving the eigenvalues of an elastic structure is optimized using a phase-field approach, which allows for topology changes and multiple materials.We show continuity and differentiability of simple eigenvalues in the phase-field co
Externí odkaz:
https://doaj.org/article/819050d9b1d74959816b80dead51fd38
Autor:
Knopf, Patrik, Stange, Jonas
This paper addresses the well-posedness of a general class of bulk-surface convective Cahn--Hilliard systems with singular potentials. For this model, we first prove the existence of a global-in-time weak solution by approximating the singular potent
Externí odkaz:
http://arxiv.org/abs/2407.14089
The main goal of this paper is to establish the nonlocal-to-local convergence of strong solutions to a Navier--Stokes--Cahn--Hilliard model with singular potential describing immiscible, viscous two-phase flows with matched densities, which is referr
Externí odkaz:
http://arxiv.org/abs/2403.10947
Autor:
Knopf, Patrik, Stange, Jonas
Publikováno v:
Nonlinear Differ. Equ. Appl. 31, 82 (2024)
We consider a general class of bulk-surface convective Cahn--Hilliard systems with dynamic boundary conditions. In contrast to classical Neumann boundary conditions, the dynamic boundary conditions of Cahn--Hilliard type allow for dynamic changes of
Externí odkaz:
http://arxiv.org/abs/2401.08400
We investigate a new diffuse-interface model that describes creeping two-phase flows (i.e., flows exhibiting a low Reynolds number), especially flows that permeate a porous medium. The system of equations consists of a Brinkman equation for the volum
Externí odkaz:
http://arxiv.org/abs/2312.15274
Publikováno v:
Discrete and Continuous Dynamical Systems - S, 2023, 16(12): 3622-3660
The Cahn--Hilliard equation with anisotropic energy contributions frequently appears in many physical systems. Systematic analytical results for the case with the relevant logarithmic free energy have been missing so far. We close this gap and show e
Externí odkaz:
http://arxiv.org/abs/2305.18255
We consider an optimization problem for the eigenvalues of a multi-material elastic structure that was previously introduced by Garcke et al. [Adv. Nonlinear Anal. 11 (2022), no. 1, 159--197]. There, the elastic structure is represented by a vector-v
Externí odkaz:
http://arxiv.org/abs/2304.02477
The Vlasov-Poisson system describes the time evolution of a plasma in the so-called collisionless regime. The investigation of a high-temperature plasma that is influenced by an exterior magnetic field is one of the most significant aspects of thermo
Externí odkaz:
http://arxiv.org/abs/2304.02083
Publikováno v:
J. Nonlinear Sci. 33 (2023) 34
We present a diffuse-interface model for the solid-state dewetting problem with anisotropic surface energies in ${\mathbb R}^d$ for $d\in\{2,3\}$. The introduced model consists of the anisotropic Cahn--Hilliard equation, with either a smooth or a dou
Externí odkaz:
http://arxiv.org/abs/2210.01698
Autor:
Giorgini, Andrea, Knopf, Patrik
Publikováno v:
Journal of Mathematical Fluid Mechanics 25:65, 2023
We derive a novel thermodynamically consistent Navier--Stokes--Cahn--Hilliard system with dynamic boundary conditions. This model describes the motion of viscous incompressible binary fluids with different densities. In contrast to previous models in
Externí odkaz:
http://arxiv.org/abs/2208.09695