@article{MTMT:33840481, title = {HYPERBOLIC LIMIT FOR A BIOLOGICAL INVASION}, url = {https://m2.mtmt.hu/api/publication/33840481}, author = {Hilhorst, Danielle and Kim, Yong Jung and Nguyen, Thanh Nam and Park, HyunJoon}, doi = {10.3934/dcdsb.2023070}, journal-iso = {DISCRETE CONT DYN-B}, journal = {DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B}, unique-id = {33840481}, issn = {1531-3492}, abstract = {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}, keywords = {population dynamics; interface problems; Reaction diffusion equations; singular perturbation; Nonlinear PDE}, year = {2023}, eissn = {1553-524X} } @article{MTMT:32965539, title = {Propagation fronts in a simplified model of tumor growth with degenerate cross-dependent self-diffusivity}, url = {https://m2.mtmt.hu/api/publication/32965539}, author = {Gallay, Thierry and Mascia, Corrado}, doi = {10.1016/j.nonrwa.2021.103387}, journal-iso = {NONLINEAR ANAL-REAL}, journal = {NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS}, volume = {63}, unique-id = {32965539}, issn = {1468-1218}, abstract = {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.}, keywords = {reaction-diffusion systems; Degenerate diffusion; traveling wave solutions; singular perturbation; Cross-dependent self-diffusivity}, year = {2022}, eissn = {1878-5719} } @article{MTMT:32293058, title = {PROPAGATING INTERFACE IN REACTION-DIFFUSION EQUATIONS WITH DISTRIBUTED DELAY}, url = {https://m2.mtmt.hu/api/publication/32293058}, author = {Wang, Haoyu and Tian, Ge}, journal-iso = {ELECTR J DIFFER EQUAT}, journal = {ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS}, unique-id = {32293058}, issn = {1072-6691}, abstract = {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.}, keywords = {TRAVELING WAVE; Distributed delay; reaction-diffusion equations; propagating interface}, year = {2021}, eissn = {1550-6150} } @article{MTMT:30904446, title = {Hole-closing model reveals exponents for nonlinear degenerate diffusivity functions in cell biology}, url = {https://m2.mtmt.hu/api/publication/30904446}, author = {McCue, Scott W. and Jin, Wang and Moroney, Timothy J. and Lo, Kai-Yin and Chou, Shih-En and Simpson, Matthew J.}, doi = {10.1016/j.physd.2019.06.005}, journal-iso = {PHYSICA D: NONLINEAR PEHONOM}, journal = {PHYSICA D: NONLINEAR PHENOMENA}, volume = {398}, unique-id = {30904446}, issn = {0167-2789}, abstract = {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.}, keywords = {Wound healing; Cell Migration Assays; Nonlinear degenerate diffusion; Porous-Fisher equation; Hole-closing problem; Self-similarity of the second kind}, year = {2019}, eissn = {1872-8022}, pages = {130-140} } @article{MTMT:27540353, title = {Nutrient-limited growth with non-linear cell diffusion as a mechanism for floral pattern formation in yeast biofilms}, url = {https://m2.mtmt.hu/api/publication/27540353}, author = {Tam, Alexander and Green, J Edward F and Balasuriya, Sanjeeva and Tek, Ee Lin and Gardner, Jennifer M and Sundstrom, Joanna F and Jiranek, Vladimir and Binder, Benjamin J}, doi = {10.1016/j.jtbi.2018.04.004}, journal-iso = {J THEOR BIOL}, journal = {JOURNAL OF THEORETICAL BIOLOGY}, volume = {448}, unique-id = {27540353}, issn = {0022-5193}, year = {2018}, eissn = {1095-8541}, pages = {122-141}, orcid-numbers = {Tam, Alexander/0000-0003-3565-1068} } @article{MTMT:26900915, title = {Inviscid traveling waves of monostable nonlinearity}, url = {https://m2.mtmt.hu/api/publication/26900915}, author = {Choi, Sun-Ho and Chung, Jaywan and Kim, Yong-Jung}, doi = {10.1016/j.aml.2017.03.019}, journal-iso = {APPL MATH LETT}, journal = {APPLIED MATHEMATICS LETTERS}, volume = {71}, unique-id = {26900915}, issn = {0893-9659}, year = {2017}, eissn = {1873-5452}, pages = {51-58} } @article{MTMT:25657735, title = {MODELING CONTACT INHIBITION OF GROWTH: TRAVELING WAVES}, url = {https://m2.mtmt.hu/api/publication/25657735}, author = {Bertsch, Michiel and Mimura, Masayasu and Wakasa, Tohru}, doi = {10.3934/nhm.2013.8.131}, journal-iso = {NETW HETEROG MEDIA}, journal = {NETWORKS AND HETEROGENEOUS MEDIA}, volume = {8}, unique-id = {25657735}, issn = {1556-1801}, year = {2013}, eissn = {1556-181X}, pages = {131-147} } @article{MTMT:25657736, title = {On the Form of Smooth-Front Travelling Waves in a Reaction-Diffusion Equation with Degenerate Nonlinear Diffusion}, url = {https://m2.mtmt.hu/api/publication/25657736}, author = {Sherratt, J A}, doi = {10.1051/mmnp/20105505}, journal-iso = {MATH MODEL NAT PHENO}, journal = {MATHEMATICAL MODELLING OF NATURAL PHENOMENA}, volume = {5}, unique-id = {25657736}, issn = {0973-5348}, year = {2010}, eissn = {1760-6101}, pages = {64-79} }