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Stability of transonic shockfronts in threedimensional conical steady potential flow past a perturbed cone
Weak shock solution in supersonic flow past a wedge
1.  School of Mathematical Sciences and Institute of Mathematics, Fudan University, Shanghai 200433, China 
[1] 
Sergey Degtyarev. Classical solvability of the multidimensional free boundary problem for the thin film equation with quadratic mobility in the case of partial wetting. Discrete & Continuous Dynamical Systems  A, 2017, 37 (7) : 36253699. doi: 10.3934/dcds.2017156 
[2] 
Toyohiko Aiki. On the existence of a weak solution to a free boundary problem for a model of a shape memory alloy spring. Discrete & Continuous Dynamical Systems  S, 2012, 5 (1) : 113. doi: 10.3934/dcdss.2012.5.1 
[3] 
Zhenhua Guo, Zilai Li. Global existence of weak solution to the free boundary problem for compressible NavierStokes. Kinetic & Related Models, 2016, 9 (1) : 75103. doi: 10.3934/krm.2016.9.75 
[4] 
GuiQiang Chen, Beixiang Fang. Stability of transonic shockfronts in threedimensional conical steady potential flow past a perturbed cone. Discrete & Continuous Dynamical Systems  A, 2009, 23 (1&2) : 85114. doi: 10.3934/dcds.2009.23.85 
[5] 
Jiayue Zheng, Shangbin Cui. Bifurcation analysis of a tumormodel free boundary problem with a nonlinear boundary condition. Discrete & Continuous Dynamical Systems  B, 2017, 22 (11) : 00. doi: 10.3934/dcdsb.2020103 
[6] 
Toyohiko Aiki. A free boundary problem for an elastic material. Conference Publications, 2007, 2007 (Special) : 1017. doi: 10.3934/proc.2007.2007.10 
[7] 
Feimin Huang, Xiaoding Shi, Yi Wang. Stability of viscous shock wave for compressible NavierStokes equations with free boundary. Kinetic & Related Models, 2010, 3 (3) : 409425. doi: 10.3934/krm.2010.3.409 
[8] 
Chonghu Guan, Fahuai Yi, Xiaoshan Chen. A fully nonlinear free boundary problem arising from optimal dividend and risk control model. Mathematical Control & Related Fields, 2019, 9 (3) : 425452. doi: 10.3934/mcrf.2019020 
[9] 
Hayk Mikayelyan, Henrik Shahgholian. Convexity of the free boundary for an exterior free boundary problem involving the perimeter. Communications on Pure & Applied Analysis, 2013, 12 (3) : 14311443. doi: 10.3934/cpaa.2013.12.1431 
[10] 
Igor Pažanin, Marcone C. Pereira. On the nonlinear convectiondiffusionreaction problem in a thin domain with a weak boundary absorption. Communications on Pure & Applied Analysis, 2018, 17 (2) : 579592. doi: 10.3934/cpaa.2018031 
[11] 
SzeBi Hsu, Bernold Fiedler, HsiuHau Lin. Classification of potential flows under renormalization group transformation. Discrete & Continuous Dynamical Systems  B, 2016, 21 (2) : 437446. doi: 10.3934/dcdsb.2016.21.437 
[12] 
Zhiguo Wang, Hua Nie, Yihong Du. Asymptotic spreading speed for the weak competition system with a free boundary. Discrete & Continuous Dynamical Systems  A, 2019, 39 (9) : 52235262. doi: 10.3934/dcds.2019213 
[13] 
Xiaoshan Chen, Fahuai Yi. Free boundary problem of Barenblatt equation in stochastic control. Discrete & Continuous Dynamical Systems  B, 2016, 21 (5) : 14211434. doi: 10.3934/dcdsb.2016003 
[14] 
Naoki Sato, Toyohiko Aiki, Yusuke Murase, Ken Shirakawa. A one dimensional free boundary problem for adsorption phenomena. Networks & Heterogeneous Media, 2014, 9 (4) : 655668. doi: 10.3934/nhm.2014.9.655 
[15] 
Yongzhi Xu. A free boundary problem model of ductal carcinoma in situ. Discrete & Continuous Dynamical Systems  B, 2004, 4 (1) : 337348. doi: 10.3934/dcdsb.2004.4.337 
[16] 
Anna Lisa Amadori. Contour enhancement via a singular free boundary problem. Conference Publications, 2007, 2007 (Special) : 4453. doi: 10.3934/proc.2007.2007.44 
[17] 
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 
[18] 
Jijun Liu, Gen Nakamura. Recovering the boundary corrosion from electrical potential distribution using partial boundary data. Inverse Problems & Imaging, 2017, 11 (3) : 521538. doi: 10.3934/ipi.2017024 
[19] 
Dimitra Antonopoulou, Georgia Karali. A nonlinear partial differential equation for the volume preserving mean curvature flow. Networks & Heterogeneous Media, 2013, 8 (1) : 922. doi: 10.3934/nhm.2013.8.9 
[20] 
Seyedeh Marzieh Ghavidel, Wolfgang M. Ruess. Flow invariance for nonautonomous nonlinear partial differential delay equations. Communications on Pure & Applied Analysis, 2012, 11 (6) : 23512369. doi: 10.3934/cpaa.2012.11.2351 
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