Xu, Shihe; Xuan, Zuxing Analysis of a free boundary problem for vascularized tumor growth with a necrotic core and time delays. (English) Zbl 1518.92049 Nonlinear Anal., Real World Appl. 72, Article ID 103855, 11 p. (2023). MSC: 92C32 35R35 PDFBibTeX XMLCite \textit{S. Xu} and \textit{Z. Xuan}, Nonlinear Anal., Real World Appl. 72, Article ID 103855, 11 p. (2023; Zbl 1518.92049) Full Text: DOI
Xu, Shihe; Zhang, Fangwei; Zhou, Qinghua A free boundary problem for necrotic tumor growth with angiogenesis. (English) Zbl 1512.35693 Appl. Anal. 102, No. 3, 977-987 (2023). MSC: 35R35 35J25 35K57 35Q92 PDFBibTeX XMLCite \textit{S. Xu} et al., Appl. Anal. 102, No. 3, 977--987 (2023; Zbl 1512.35693) Full Text: DOI
Lu, Min-Jhe; Hao, Wenrui; Hu, Bei; Li, Shuwang Bifurcation analysis of a free boundary model of vascular tumor growth with a necrotic core and chemotaxis. (English) Zbl 1506.35008 J. Math. Biol. 86, No. 1, Paper No. 19, 28 p. (2023). MSC: 35B32 35B35 35K57 35R35 35Q92 PDFBibTeX XMLCite \textit{M.-J. Lu} et al., J. Math. Biol. 86, No. 1, Paper No. 19, 28 p. (2023; Zbl 1506.35008) Full Text: DOI arXiv
Zhao, Zhiwen Asymptotic analysis for the electric field concentration with geometry of the core-shell structure. (English) Zbl 1487.78015 Commun. Pure Appl. Anal. 21, No. 4, 1109-1137 (2022). MSC: 78A48 35B44 35C20 35B65 35J25 78M35 35Q60 PDFBibTeX XMLCite \textit{Z. Zhao}, Commun. Pure Appl. Anal. 21, No. 4, 1109--1137 (2022; Zbl 1487.78015) Full Text: DOI
Hingyi, B.; Karátson, J. Detection of dead cores for reaction-diffusion equations with a non-smooth nonlinearity. (English) Zbl 1484.65299 Appl. Numer. Math. 177, 111-122 (2022). MSC: 65N30 35J92 65N12 PDFBibTeX XMLCite \textit{B. Hingyi} and \textit{J. Karátson}, Appl. Numer. Math. 177, 111--122 (2022; Zbl 1484.65299) Full Text: DOI
Song, Huijuan; Hu, Bei; Wang, Zejia Stationary solutions of a free boundary problem modeling the growth of vascular tumors with a necrotic core. (English) Zbl 1465.35420 Discrete Contin. Dyn. Syst., Ser. B 26, No. 1, 667-691 (2021). MSC: 35R35 35K57 35B32 35B35 92B05 PDFBibTeX XMLCite \textit{H. Song} et al., Discrete Contin. Dyn. Syst., Ser. B 26, No. 1, 667--691 (2021; Zbl 1465.35420) Full Text: DOI arXiv
Babb, T.; Benham, G. P.; Bows, J.; Gonzalez-Farina, R.; Kiradjiev, K. B.; Lee, W. T.; Tibos, S. Predicting lift-off time when deep-frying potato dough snacks. (English) Zbl 1468.80003 SIAM J. Appl. Math. 81, No. 2, 574-590 (2021). Reviewer: Aleksey Syromyasov (Saransk) MSC: 80A22 80A19 80M35 35B40 PDFBibTeX XMLCite \textit{T. Babb} et al., SIAM J. Appl. Math. 81, No. 2, 574--590 (2021; Zbl 1468.80003) Full Text: DOI arXiv
Xu, Shihe; Su, Dan Analysis of necrotic core formation in angiogenic tumor growth. (English) Zbl 1430.92027 Nonlinear Anal., Real World Appl. 51, Article ID 103016, 12 p. (2020). MSC: 92C32 92C15 35Q92 35B40 35R35 PDFBibTeX XMLCite \textit{S. Xu} and \textit{D. Su}, Nonlinear Anal., Real World Appl. 51, Article ID 103016, 12 p. (2020; Zbl 1430.92027) Full Text: DOI
da Silva, João Vítor; Salort, Ariel M. Sharp regularity estimates for quasi-linear elliptic dead core problems and applications. (English) Zbl 1398.35081 Calc. Var. Partial Differ. Equ. 57, No. 3, Paper No. 83, 1-24 (2018). Reviewer: Dian K. Palagachev (Bari) MSC: 35J62 35B65 PDFBibTeX XMLCite \textit{J. V. da Silva} and \textit{A. M. Salort}, Calc. Var. Partial Differ. Equ. 57, No. 3, Paper No. 83, 1--24 (2018; Zbl 1398.35081) Full Text: DOI
Teixeira, Eduardo V. Regularity for the fully nonlinear dead-core problem. (English) Zbl 1336.35195 Math. Ann. 364, No. 3-4, 1121-1134 (2016). Reviewer: Mariana Vega Smit (Essen) MSC: 35K55 35K57 35B65 PDFBibTeX XMLCite \textit{E. V. Teixeira}, Math. Ann. 364, No. 3--4, 1121--1134 (2016; Zbl 1336.35195) Full Text: DOI
Ansoni, J. L.; Brandi, A. C.; Seleghim, P. jun Resolution of an inverse thermal problem using parallel processing on shared-memory multiprocessor architectures. (English) Zbl 1328.65229 Inverse Probl. Sci. Eng. 23, No. 2, 351-375 (2015). MSC: 65N21 65Y05 35J05 35R30 65N30 65F10 PDFBibTeX XMLCite \textit{J. L. Ansoni} et al., Inverse Probl. Sci. Eng. 23, No. 2, 351--375 (2015; Zbl 1328.65229) Full Text: DOI
Pourgholi, Reza; Esfahani, Amin; Dana, Hassan Real valued genetic algorithm for solving an inverse hyperbolic problem: multi-core parallelisation approach. (English) Zbl 1301.65102 Int. J. Math. Model. Numer. Optim. 4, No. 4, 410-424 (2013). MSC: 65M32 35L20 35R30 65M06 65Y05 PDFBibTeX XMLCite \textit{R. Pourgholi} et al., Int. J. Math. Model. Numer. Optim. 4, No. 4, 410--424 (2013; Zbl 1301.65102) Full Text: DOI
Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Liu, Yuan; Sommese, Andrew J.; Zhang, Yong-Tao Bifurcation for a free boundary problem modeling the growth of a tumor with a necrotic core. (English) Zbl 1238.35193 Nonlinear Anal., Real World Appl. 13, No. 2, 694-709 (2012). MSC: 35R35 35Q92 92C50 35K40 35B32 PDFBibTeX XMLCite \textit{W. Hao} et al., Nonlinear Anal., Real World Appl. 13, No. 2, 694--709 (2012; Zbl 1238.35193) Full Text: DOI
Lee, Shin-Yi; Wang, Shin-Wa; Ye, Chiou-Ping Explicit necessary and sufficient conditions for the existence of a dead core solution of a \(p\)-Laplacian steady-state reaction-diffusion problem. (English) Zbl 1141.35381 Discrete Contin. Dyn. Syst. 2005, Suppl., 587-596 (2005). MSC: 35J65 34B15 PDFBibTeX XMLCite \textit{S.-Y. Lee} et al., Discrete Contin. Dyn. Syst. 2005, 587--596 (2005; Zbl 1141.35381)
Takeuchi, Shingo; Yamada, Yoshio Asymptotic properties of a reaction-diffusion equation with degenerate \(p\)-Laplacian. (English) Zbl 0961.35075 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 42, No. 1, 41-61 (2000). Reviewer: Vladimir N.Grebenev (Novosibirsk) MSC: 35K65 35B32 35B40 35B45 35B05 PDFBibTeX XMLCite \textit{S. Takeuchi} and \textit{Y. Yamada}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 42, No. 1, 41--61 (2000; Zbl 0961.35075) Full Text: DOI
Cercignani, C.; Gerasimenko, V. I.; Petrina, D. Ya. Many-particle dynamics and kinetic equations. (English) Zbl 0933.82001 Mathematics and its Applications (Dordrecht). 420. Dordrecht: Kluwer Academic Publishers. viii, 244 p. (1997). Reviewer: S.Poghosyan (Erevan) MSC: 82-02 82C40 35Q99 76P05 45K05 PDFBibTeX XMLCite \textit{C. Cercignani} et al., Many-particle dynamics and kinetic equations. Dordrecht: Kluwer Academic Publishers (1997; Zbl 0933.82001)
Cui, Shangbin Dead core problem for semilinear elliptic and parabolic equations having divergence terms. (Chinese. English summary) Zbl 0835.35009 J. Syst. Sci. Math. Sci. 14, No. 2, 102-108 (1994). Reviewer: Li Mingzhong (Shanghai) MSC: 35B05 35J60 35K55 PDFBibTeX XMLCite \textit{S. Cui}, J. Syst. Sci. Math. Sci. 14, No. 2, 102--108 (1994; Zbl 0835.35009)
Di Liddo, A. The dead-core in a single reaction with lumped temperature. (English) Zbl 0799.92026 Chadam, John M. (ed.) et al., Emerging applications in free boundary problems. Proceedings of the international colloquium “Free boundary problems: theory and applications”, held in Montreal, Canada, June 13 - June 22, 1990. Harlow, Essex: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 280, 181-187 (1993). Reviewer: D.Dorninger (Wien) MSC: 92E20 35Q92 35K57 PDFBibTeX XMLCite \textit{A. Di Liddo}, Pitman Res. Notes Math. Ser. 280, 181--187 (1993; Zbl 0799.92026)
Chan, C. Y.; Fung, David T. Dead cores and effectiveness of semilinear reaction-diffusion systems. (English) Zbl 0780.35037 J. Math. Anal. Appl. 171, No. 2, 498-515 (1992). Reviewer: S.Jimbo (Sapporo) MSC: 35J65 35K57 35B05 PDFBibTeX XMLCite \textit{C. Y. Chan} and \textit{D. T. Fung}, J. Math. Anal. Appl. 171, No. 2, 498--515 (1992; Zbl 0780.35037) Full Text: DOI
Bernoff, Andrew J. Spiral wave solutions for reaction-diffusion equations in a fast reaction/slow diffusion limit. (English) Zbl 0744.35057 Physica D 53, No. 1, 125-150 (1991). MSC: 35Q80 35K57 PDFBibTeX XMLCite \textit{A. J. Bernoff}, Physica D 53, No. 1, 125--150 (1991; Zbl 0744.35057) Full Text: DOI
Bobisud, L. E. Steady-state turbulent flow with reaction. (English) Zbl 0760.34023 Rocky Mt. J. Math. 21, No. 3, 993-1007 (1991). MSC: 34B15 76S05 35K57 PDFBibTeX XMLCite \textit{L. E. Bobisud}, Rocky Mt. J. Math. 21, No. 3, 993--1007 (1991; Zbl 0760.34023) Full Text: DOI
Stakgold, I. Localization and extinction in reaction-diffusion. (English) Zbl 0724.35054 Free boundary problems: theory and applications, Proc. Int. Colloq., Irsee/Ger. 1987, Vol. I, Pitman Res. Notes Math. Ser. 185, 208-221 (1990). Reviewer: I.Stakgold MSC: 35K57 35J65 35B05 80A25 PDFBibTeX XML
Ricci, Riccardo; Tarzia, Domingo A. Asymptotic behavior of the solutions of the dead-core problem. (English) Zbl 0699.35022 Nonlinear Anal., Theory Methods Appl. 13, No. 4, 405-411 (1989). Reviewer: H.Lange MSC: 35B40 35K57 35K20 35A30 PDFBibTeX XMLCite \textit{R. Ricci} and \textit{D. A. Tarzia}, Nonlinear Anal., Theory Methods Appl. 13, No. 4, 405--411 (1989; Zbl 0699.35022) Full Text: DOI
Ambrosetti, A.; Struwe, M. Existence of steady vortex rings in an ideal fluid. (English) Zbl 0694.76012 Arch. Ration. Mech. Anal. 108, No. 2, 97-109 (1989). MSC: 76B47 35Q30 PDFBibTeX XMLCite \textit{A. Ambrosetti} and \textit{M. Struwe}, Arch. Ration. Mech. Anal. 108, No. 2, 97--109 (1989; Zbl 0694.76012) Full Text: DOI
Rogers, C.; McInnis, C.; Rasmussen, H. On a Stefan problem involving a special spherical region: Application of a Bergman-type expansion. (English) Zbl 0624.65127 Appl. Math. Comput. 18, 143-154 (1986). Reviewer: P.-L.Lions MSC: 65Z05 65N35 35R35 35K60 80A17 PDFBibTeX XMLCite \textit{C. Rogers} et al., Appl. Math. Comput. 18, 143--154 (1986; Zbl 0624.65127) Full Text: DOI
Garg, N. K.; Taylor, C. Symmetrization of matrix technique in a finite element context. (English) Zbl 0601.65080 Appl. Math. Modelling 9, 234-238 (1985). Reviewer: M.Bernadou MSC: 65N30 65F10 35K20 35Q30 76D05 PDFBibTeX XMLCite \textit{N. K. Garg} and \textit{C. Taylor}, Appl. Math. Modelling 9, 234--238 (1985; Zbl 0601.65080) Full Text: DOI
Bandle, C.; Stakgold, I. Reaction-diffusion and dead cores. (English) Zbl 0594.35058 Free boundary problems: applications and theory, Vol. IV, Proc. Int. Colloq., Maubuisson/France 1984, Res. Notes Math. 121, 436-448 (1985). MSC: 35K60 35A05 35B40 35R35 PDFBibTeX XML
Kawohl, Bernhard When are solutions to nonlinear elliptic boundary value problems convex? (English) Zbl 0587.35026 Commun. Partial Differ. Equations 10, 1213-1225 (1985). Reviewer: M.Kučera MSC: 35J25 35J60 35B50 PDFBibTeX XMLCite \textit{B. Kawohl}, Commun. Partial Differ. Equations 10, 1213--1225 (1985; Zbl 0587.35026) Full Text: DOI
Díaz Díaz, Gregorio Properties of maximum principle type for \(F(x,u,D^ 2u)=0\). (Spanish) Zbl 0574.35035 Differential equations and applications, Proc. 7th Congr., Granada/Spain 1984, 143-148 (1985). Reviewer: J.Hernández MSC: 35J65 35J70 35B50 PDFBibTeX XML
Friedman, Avner; Phillips, Daniel The free boundary of a semilinear elliptic equation. (English) Zbl 0552.35079 Trans. Am. Math. Soc. 282, 153-182 (1984). Reviewer: R.Landes MSC: 35R35 35J65 35J20 PDFBibTeX XMLCite \textit{A. Friedman} and \textit{D. Phillips}, Trans. Am. Math. Soc. 282, 153--182 (1984; Zbl 0552.35079) Full Text: DOI
Bandle, C.; Sperb, R. P.; Stakgold, I. Diffusion and reaction with monotone kinetics. (English) Zbl 0545.35011 Nonlinear Anal., Theory Methods Appl. 8, 321-333 (1984). MSC: 35B45 35J60 35B50 PDFBibTeX XMLCite \textit{C. Bandle} et al., Nonlinear Anal., Theory Methods Appl. 8, 321--333 (1984; Zbl 0545.35011) Full Text: DOI