Second-order sufficient conditions in the sparse optimal control of a phase field tumor growth model with logarithmic potential [PDF]
E S A I M: Control, Optimisation and Calculus of Variations, 2023 This paper treats a distributed optimal control problem for a tumor growth model of viscous Cahn--Hilliard type. The evolution of the tumor fraction is governed by a thermodynamic force induced by a double-well potential of logarithmic type.
J. Sprekels, F. Troltzsch
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Convergence rate for the incompressible limit of nonlinear diffusion–advection equations [PDF]
Annales de l'Institut Henri Poincare. Analyse non linéar, 2021 The incompressible limit of nonlinear diffusion equations of porous medium type has attracted a lot of attention in recent years, due to its ability to link the weak formulation of cell-population models to free boundary problems of Hele-Shaw type ...
Noemi David, Tomasz Dkebiec, B. Perthame
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Existence of Solutions to the Poisson-Nernst-Planck System with Singular Permanent Charges in $\mathbb{R}^2$ [PDF]
SIAM Journal on Mathematical Analysis, 2021 In this paper, we study the well-posedness of Poisson–Nernst–Planck system with no-flux boundary condition and singular permanent charges in two dimension. The main difficulty comes from the lack of integrability of singular permanent charges.
C. Hsieh, Yongjiang Yu
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Quantitative Estimates of the Threshold Phenomena for Propagation in Reaction-Diffusion Equations [PDF]
SIAM Journal on Applied Dynamical Systems, 2019 We focus on the (sharp) threshold phenomena arising in some reaction-diffusion equations supplemented with some compactly supported initial data. In the so-called ignition and bistable cases, we prove the first sharp quantitative estimate on the (sharp ...
M. Alfaro, A. Ducrot, Grégory Faye
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Port-Hamiltonian model of two-dimensional shallow water equations in moving containers
IMA Journal of Mathematical Control and Information, 2020 The free surface motion in moving containers is an important physical phenomenon for many engineering applications. One way to model the free surface motion is by employing shallow water equations (SWEs).
F. Cardoso-Ribeiro +2 more
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Advantage and Disadvantage of Dispersal in Two-Species Competition Models
CSIAM Transactions on Applied Mathematics, 2020 We consider a two-species competition model in which both populations are identical except their movement strategies: One species moves upward along the fitness gradient, while the other does not diffuse.
M. Lou
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Front propagation in a double degenerate equation with delay
Advances in Nonlinear Analysis, 2023 The current article is concerned with the traveling fronts for a class of double degenerate equations with delay. We first show that the traveling fronts decay algebraically at one end, while those may decay exponentially or algebraically at the other ...
Bo Wei-Jian, Wu Shi-Liang, Du Li-Jun
doaj +1 more source
On the geometric diversity of wavefronts for the scalar Kolmogorov ecological equation [PDF]
Journal of Nonlinear Science (2020), 2019 In this work, we answer three fundamental questions concerning monostable travelling fronts for the scalar Kolmogorov ecological equation with diffusion and spatiotemporal interaction: these are the questions about their existence, uniqueness and geometric shape.
arxiv +1 more source
On a class of nonlinear reaction‐diffusion systems with nonlocal boundary conditions
Abstract and Applied Analysis, Volume 2004, Issue 9, Page 793-813, 2004., 2004 We prove the existence, uniqueness, and continuous dependence of a generalized solution of a nonlinear reaction‐diffusion system with only integral terms in the boundaries. We first solve a particular case of the problem by using the energy‐integral method. Next, via an iteration procedure, we derive the obtained results to study the solvability of the
Abdelfatah Bouziani
wiley +1 more source
On controllability, parametrization, and output tracking of a linearized bioreactor model
Journal of Applied Mathematics, Volume 2003, Issue 5, Page 243-276, 2003., 2003 The paper deals with a distributed parameter system related to the so‐called fixed‐bed bioreactor. The original nonlinear partial differential system is linearized around the steady state. We find that the linearized system is not exactly controllable but it is approximatively controllable when certain algebraic equations hold.
J. Tervo, M. T. Nihtilä, P. Kokkonen
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