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On shock waves in solids
Nonlinear threedimensional simulation of solid tumor growth
1.  Department of Mathematics, University of California, Irvine, CA 92697, United States 
2.  School of Health Information Sciences, University of Texas Health Science Center, Houston, TX 77030, United States 
3.  Center for Mathematical and Computational Biology, Department of Mathematics, University of California, Irvine, CA 926973875 
4.  Department of Mathematics, Center for Mathematical and Computational Biology, University of California, Irvine, CA 92697, United States 
[1] 
Thomas Y. Hou, Pingwen Zhang. Convergence of a boundary integral method for 3D water waves. Discrete & Continuous Dynamical Systems  B, 2002, 2 (1) : 134. doi: 10.3934/dcdsb.2002.2.1 
[2] 
Yi Shi, Kai Bao, XiaoPing Wang. 3D adaptive finite element method for a phase field model for the moving contact line problems. Inverse Problems & Imaging, 2013, 7 (3) : 947959. doi: 10.3934/ipi.2013.7.947 
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Guoliang Ju, Can Chen, Rongliang Chen, Jingzhi Li, Kaitai Li, Shaohui Zhang. Numerical simulation for 3D flow in flow channel of aeroengine turbine fan based on dimension splitting method. Electronic Research Archive, 2020, 28 (2) : 837851. doi: 10.3934/era.2020043 
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Thomas Y. Hou, Zuoqiang Shi. Dynamic growth estimates of maximum vorticity for 3D incompressible Euler equations and the SQG model. Discrete & Continuous Dynamical Systems, 2012, 32 (5) : 14491463. doi: 10.3934/dcds.2012.32.1449 
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Nikodem J. Poplawski, Abbas Shirinifard, Maciej Swat, James A. Glazier. Simulation of singlespecies bacterialbiofilm growth using the GlazierGranerHogeweg model and the CompuCell3D modeling environment. Mathematical Biosciences & Engineering, 2008, 5 (2) : 355388. doi: 10.3934/mbe.2008.5.355 
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Michael V. Klibanov, DinhLiem Nguyen, Loc H. Nguyen, Hui Liu. A globally convergent numerical method for a 3D coefficient inverse problem with a single measurement of multifrequency data. Inverse Problems & Imaging, 2018, 12 (2) : 493523. doi: 10.3934/ipi.2018021 
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Shijin Ding, Zhilin Lin, Dongjuan Niu. Boundary layer for 3D plane parallel channel flows of nonhomogeneous incompressible NavierStokes equations. Discrete & Continuous Dynamical Systems, 2020, 40 (8) : 45794596. doi: 10.3934/dcds.2020193 
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A. V. Fursikov. Stabilization for the 3D NavierStokes system by feedback boundary control. Discrete & Continuous Dynamical Systems, 2004, 10 (1&2) : 289314. doi: 10.3934/dcds.2004.10.289 
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Anna Kostianko, Sergey Zelik. Inertial manifolds for the 3D CahnHilliard equations with periodic boundary conditions. Communications on Pure & Applied Analysis, 2015, 14 (5) : 20692094. doi: 10.3934/cpaa.2015.14.2069 
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Mei Wang, Zilai Li, Zhenhua Guo. Global weak solution to 3D compressible flows with densitydependent viscosity and free boundary. Communications on Pure & Applied Analysis, 2017, 16 (1) : 124. doi: 10.3934/cpaa.2017001 
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Marcelo M. Disconzi, Igor Kukavica. A priori estimates for the 3D compressible freeboundary Euler equations with surface tension in the case of a liquid. Evolution Equations & Control Theory, 2019, 8 (3) : 503542. doi: 10.3934/eect.2019025 
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Boyan Jonov, Thomas C. Sideris. Global and almost global existence of small solutions to a dissipative wave equation in 3D with nearly null nonlinear terms. Communications on Pure & Applied Analysis, 2015, 14 (4) : 14071442. doi: 10.3934/cpaa.2015.14.1407 
[14] 
Yaodan Huang, Zhengce Zhang, Bei Hu. Bifurcation from stability to instability for a free boundary tumor model with angiogenesis. Discrete & Continuous Dynamical Systems, 2019, 39 (5) : 24732510. doi: 10.3934/dcds.2019105 
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Niklas Hartung. Efficient resolution of metastatic tumor growth models by reformulation into integral equations. Discrete & Continuous Dynamical Systems  B, 2015, 20 (2) : 445467. doi: 10.3934/dcdsb.2015.20.445 
[16] 
Shihe Xu. Analysis of a delayed free boundary problem for tumor growth. Discrete & Continuous Dynamical Systems  B, 2011, 15 (1) : 293308. doi: 10.3934/dcdsb.2011.15.293 
[17] 
Yong Zhou. Remarks on regularities for the 3D MHD equations. Discrete & Continuous Dynamical Systems, 2005, 12 (5) : 881886. doi: 10.3934/dcds.2005.12.881 
[18] 
HyeongOhk Bae, Bum Ja Jin. Estimates of the wake for the 3D Oseen equations. Discrete & Continuous Dynamical Systems  B, 2008, 10 (1) : 118. doi: 10.3934/dcdsb.2008.10.1 
[19] 
Indranil SenGupta, Weisheng Jiang, Bo Sun, Maria Christina Mariani. Superradiance problem in a 3D annular domain. Conference Publications, 2011, 2011 (Special) : 13091318. doi: 10.3934/proc.2011.2011.1309 
[20] 
Giovanny Guerrero, José Antonio Langa, Antonio Suárez. Biodiversity and vulnerability in a 3D mutualistic system. Discrete & Continuous Dynamical Systems, 2014, 34 (10) : 41074126. doi: 10.3934/dcds.2014.34.4107 
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