TY - JOUR AU - Hilhorst, Danielle AU - Kim, Yong Jung AU - Nguyen, Thanh Nam AU - Park, HyunJoon TI - HYPERBOLIC LIMIT FOR A BIOLOGICAL INVASION JF - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B J2 - DISCRETE CONT DYN-B PY - 2023 PG - 17 SN - 1531-3492 DO - 10.3934/dcdsb.2023070 UR - https://m2.mtmt.hu/api/publication/33840481 ID - 33840481 AB - In a spatially heterogeneous environment the propagation speed of a biological invasion varies in space. The traveling wave theory in a homogeneous case is not extended to a heterogeneous case. Taking a singular limit in a hyperbolic scale is a good way to study such a wave propagation with constant speed. The goal of this project is to understand the effect of biological diffusion on the wave speed in a spatial heterogeneous environment. For this purpose, we consider LA - English DB - MTMT ER - TY - JOUR AU - Gallay, Thierry AU - Mascia, Corrado TI - Propagation fronts in a simplified model of tumor growth with degenerate cross-dependent self-diffusivity JF - NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS J2 - NONLINEAR ANAL-REAL VL - 63 PY - 2022 PG - 28 SN - 1468-1218 DO - 10.1016/j.nonrwa.2021.103387 UR - https://m2.mtmt.hu/api/publication/32965539 ID - 32965539 AB - Motivated by tumor growth in Cancer Biology, we provide a complete analysis of existence and non-existence of invasive fronts for the reduced Gatenby-Gawlinski modelpartial derivative U-t = U {f (U) -dV } , partial derivative V-t = partial differential x {f (U) partial differential xV } + rV f (V ),where f(u) = 1 - u and the parameters d, r are positive. Denoting by (U, V) the traveling wave profile and by (U +/-, V +/-) its asymptotic states at +/-infinity, we investigate existence in the regimesd < 1: (u-, v-) = (1 - d,1) and (u(+), v(+)) = (1, 0), d < 1: (u-, v-) = (1 - d,1) and (u(+), v(+)) = (1, 0),which are called, respectively, homogeneous invasion and heterogeneous invasion. In both cases, we prove that a propagating front exists whenever the speed parameter c is strictly positive. We also derive an accurate approximation of the front profile in the singular limit c -> 0. (C) 2021 Elsevier Ltd. All rights reserved. LA - English DB - MTMT ER - TY - JOUR AU - Wang, Haoyu AU - Tian, Ge TI - PROPAGATING INTERFACE IN REACTION-DIFFUSION EQUATIONS WITH DISTRIBUTED DELAY JF - ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS J2 - ELECTR J DIFFER EQUAT PY - 2021 PG - 22 SN - 1072-6691 UR - https://m2.mtmt.hu/api/publication/32293058 ID - 32293058 AB - This article concerns the limiting behavior of the solution to a reaction-diffusion equation with distributed delay. We firstly consider the quasi-monotone situation and then investigate the non-monotone situation by constructing two auxiliary quasi-monotone equations. The limit behaviors of solutions of the equation can be obtained from the sandwich technique and the comparison principle of the Cauchy problem. It is proved that the propagation speed of the interface is equal to the minimum wave speed of the corresponding traveling waves. This makes possible to observe the minimum speed of traveling waves from a new perspective. LA - English DB - MTMT ER - TY - JOUR AU - McCue, Scott W. AU - Jin, Wang AU - Moroney, Timothy J. AU - Lo, Kai-Yin AU - Chou, Shih-En AU - Simpson, Matthew J. TI - Hole-closing model reveals exponents for nonlinear degenerate diffusivity functions in cell biology JF - PHYSICA D: NONLINEAR PHENOMENA J2 - PHYSICA D: NONLINEAR PEHONOM VL - 398 PY - 2019 SP - 130 EP - 140 PG - 11 SN - 0167-2789 DO - 10.1016/j.physd.2019.06.005 UR - https://m2.mtmt.hu/api/publication/30904446 ID - 30904446 AB - Continuum mathematical models for collective cell motion normally involve reaction-diffusion equations, such as the Fisher-KPP equation, with a linear diffusion term to describe cell motility and a logistic term to describe cell proliferation. While the Fisher-KPP equation and its generalisations are commonplace, a significant drawback for this family of models is that they are not able to capture the moving fronts that arise in cell invasion applications such as wound healing and tumour growth. An alternative, less common, approach is to include nonlinear degenerate diffusion in the models, such as in the Porous-Fisher equation, since solutions to the corresponding equations have compact support and therefore explicitly allow for moving fronts. We consider here a hole-closing problem for the Porous-Fisher equation whereby there is initially a simply connected region (the hole) with a nonzero population outside of the hole and a zero population inside. We outline how self-similar solutions (of the second kind) describe both circular and non-circular fronts in the hole-closing limit. Further, we present new experimental and theoretical evidence to support the use of nonlinear degenerate diffusion in models for collective cell motion. Our methodology involves setting up a two-dimensional wound healing assay that has the geometry of a hole-closing problem, with cells initially seeded outside of a hole that closes as cells migrate and proliferate. For a particular class of fibroblast cells, the aspect ratio of an initially rectangular wound increases in time, so the wound becomes longer and thinner as it closes; our theoretical analysis shows that this behaviour is consistent with nonlinear degenerate diffusion but is not able to be captured with commonly used linear diffusion. This work is important because it provides a clear test for degenerate diffusion over linear diffusion in cell lines, whereas standard one-dimensional experiments are unfortunately not capable of distinguishing between the two approaches. (C) 2019 Elsevier B.V. All rights reserved. LA - English DB - MTMT ER - TY - JOUR AU - Tam, Alexander AU - Green, J Edward F AU - Balasuriya, Sanjeeva AU - Tek, Ee Lin AU - Gardner, Jennifer M AU - Sundstrom, Joanna F AU - Jiranek, Vladimir AU - Binder, Benjamin J TI - Nutrient-limited growth with non-linear cell diffusion as a mechanism for floral pattern formation in yeast biofilms JF - JOURNAL OF THEORETICAL BIOLOGY J2 - J THEOR BIOL VL - 448 PY - 2018 SP - 122 EP - 141 PG - 20 SN - 0022-5193 DO - 10.1016/j.jtbi.2018.04.004 UR - https://m2.mtmt.hu/api/publication/27540353 ID - 27540353 LA - English DB - MTMT ER - TY - JOUR AU - Choi, Sun-Ho AU - Chung, Jaywan AU - Kim, Yong-Jung TI - Inviscid traveling waves of monostable nonlinearity JF - APPLIED MATHEMATICS LETTERS J2 - APPL MATH LETT VL - 71 PY - 2017 SP - 51 EP - 58 PG - 8 SN - 0893-9659 DO - 10.1016/j.aml.2017.03.019 UR - https://m2.mtmt.hu/api/publication/26900915 ID - 26900915 LA - English DB - MTMT ER - TY - JOUR AU - Bertsch, Michiel AU - Mimura, Masayasu AU - Wakasa, Tohru TI - MODELING CONTACT INHIBITION OF GROWTH: TRAVELING WAVES JF - NETWORKS AND HETEROGENEOUS MEDIA J2 - NETW HETEROG MEDIA VL - 8 PY - 2013 IS - 1 SP - 131 EP - 147 PG - 17 SN - 1556-1801 DO - 10.3934/nhm.2013.8.131 UR - https://m2.mtmt.hu/api/publication/25657735 ID - 25657735 LA - English DB - MTMT ER - TY - JOUR AU - Sherratt, J A TI - On the Form of Smooth-Front Travelling Waves in a Reaction-Diffusion Equation with Degenerate Nonlinear Diffusion JF - MATHEMATICAL MODELLING OF NATURAL PHENOMENA J2 - MATH MODEL NAT PHENO VL - 5 PY - 2010 IS - 5 SP - 64 EP - 79 PG - 16 SN - 0973-5348 DO - 10.1051/mmnp/20105505 UR - https://m2.mtmt.hu/api/publication/25657736 ID - 25657736 LA - English DB - MTMT ER -