The impact factors of the risk index and diffusive dynamics of a SIS free boundary model [PDF]
Infectious Disease Modelling, 2022 To discuss the impact factors on the spread of infectious diseases, we study a free boundary problem describing a SIS (susceptible-infected-susceptible) model in a heterogeneous environment.
Yachun Tong, Inkyung Ahn, Zhigui Lin
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Qualitative analysis of a reaction-diffusion SIRS epidemic model with nonlinear incidence rate and partial immunity [PDF]
Infectious Disease Modelling, 2023 In this paper, a reaction-diffusion SIRS epidemic model with nonlinear incidence rate and partial immunity in a spatially heterogeneous environment is proposed. The well-posedness of the solution is firstly established. Then the basic reproduction number
Jianpeng Wang +2 more
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Computation of solution to fractional order partial reaction diffusion equations [PDF]
Journal of Advanced Research, 2020 In this article, the considered problem of Cauchy reaction diffusion equation of fractional order is solved by using integral transform of Laplace coupled with decomposition technique due to Adomian scheme.
Haji Gul +4 more
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Analysis of a diffusive two-strain malaria model with the carrying capacity of the environment for mosquitoes [PDF]
Infectious Disease ModellingWe propose a malaria model involving the sensitive and resistant strains, which is described by reaction-diffusion equations. The model reflects the scenario that the vector and host populations disperse with distinct diffusion rates, susceptible ...
Jinliang Wang, Wenjing Wu, Yuming Chen
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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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Non-autonomous weighted elliptic equations with double exponential growth
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 We consider the existence of solutions of the following weighted problem: {L:=-div(ρ(x)|∇u|N-2∇u)+ξ(x)|u|N-2u=f(x,u)inBu>0inBu=0on∂B,\left\{ {\matrix{{L: = - div\left( {\rho \left( x \right){{\left| {\nabla u} \right|}^{N - 2}}\nabla u} \right) + \xi ...
Baraket Sami, Jaidane Rached
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The regularity of weak solutions for certain n-dimensional strongly coupled parabolic systems
Advanced Nonlinear Studies, 2022 This paper is concerned with the n-dimensional strongly coupled parabolic systems with triangular form in the cylinder Ω×(0,T]\Omega \times (0,T]. We investigate L2{L}^{2} and Hölder regularity of the derivatives of weak solutions (u1,u2)\left({u}_{1},{u}
Tan Qi-Jian
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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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