[1] Abels H, Butz J. Short time existence for the curve diffusion flow with a contact angle. J Differential Equations, 2019, 268(1): 318-352
[2] Abramowitz M, Stegun I A.Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Washington DC: National Bureau of Standards, 1964
[3] Albuquerque Y F, Laurain A, Sturm K. A shape optimization approach for electrical impedance tomography with point measurements. Inverse Problems, 2020, 36(9): 095006
[4] Amann H, Fila M. A Fujita-type theorem for the Laplace equation with a dynamical boundary condition. Acta Math Univ Comeniane, 1997, 56(2): 321-328
[5] Arendt W, Ter Elst A F M. The Dirichlet-to-Neumann operator on rough domains. J Differential Equations, 2011, 251(8): 2100-2124
[6] Arendt W, Ter Elst A F M, Warma M. Fractional powers of sectorial operators via the Dirichlet-to-Neumann operator. Comm Partial Differential Equations, 2018, 43(1): 1-24
[7] Barrios B, Colorado E, Pablo A D, S$\acute{\rm a}$nchez U. On some critical problems for the fractional Laplacian operator. J Differential Equations, 2012, 252(11): 6133-6162
[8] Biler P, Pilarczyk D. Around a singular solution of a nonlocal nonlinear heat equation. Nonlinear Differ Equ Appl, 2019, 26(1): 1-24
[9] Borcea L, Gray G A, Zhang Y. Variationally constrained numerical solution of electrical impedance tomography. Inverse Problems, 2003, 19(5): 1159-1184
[10] Brándle C, Colorado E, Pablo A D. A concave-convex elliptic problem involving the fractional Laplacian. Proc Roy Soc Edinburgh Sect A, 2013, 143(1): 39-71
[11] Brezis H, Lieb E. A relation between pointwise convergence of functions and convergence of functionals. Proc Amer Math Soc, 1983, 88(3): 486-486
[12] Brezis H. Elliptic equations with limiting Sobolev exponents-the impact of topology. Comm Pure Appl Math, 1986, 39(S1): S17-S39
[13] Cabré X, Tan J G. Positive solutions of nonlinear problems involving the square root of the Laplacian. Adv Math, 2010, 224(5): 2052-2093
[14] Caffarelli L, Silvestre L. An extension problem related to the fractional Laplacian. Comm Partial Differential Equations, 2007, 32(8): 1245-1260
[15] Capella A, Dávila J Dupaigne L,et al. Regularity of radial extremal solutions for some non-local semilinear equations. Comm Partial Differential Equations,2011, 36(8): 1353-1384
[16] Cazenave T, Lions P L. Solutions globales d'Equations de la chaleur semilineaires. Commun in Partial Differential Equations, 1984, 9(10): 955-978
[17] Chen G Y, Wei J C, Zhou Y F. Finite time blow-up for the fractional critical heat equation in $R^n$. Nonlinear Anal, 2019, 193: 111420
[18] Chen W X, Li C M, Ou B. Classification of solutions for an integral equation. Comm Pure Appl Math, 2006, 59(3): 330-343
[19] Chen W X, Qi S J. Direct methods on fractional equations. Discrete Contin Dyn Syst, 2019, 39(3): 1269-1310
[20] Choi W, Kim S, Lee K A. Asymptotic behavior of solutions for nonlinear elliptic problems with the fractional Laplacian. J Funct Anal, 2014, 266: 6531-6598
[21] Cherif M A, El Arwadi T, Emamirad H, Sac-épée J M. Dirichlet-to-Neumann semigroup acts as a magnifying glass. Semigroup Forum,2014, 88(3): 753-767
[22] Daners D. Non-positivity of the semigroup generated by the Dirichlet-to-Neumann operator. Positivity, 2014, 18: 235-256
[23] Du S Z. On partial regularity of the borderline solution of the semilinear parabolic equation with critical growth. Adv Differential Equations, 2013, 18(1/2): 147-177
[24] Escher J. Nonlinear elliptic systems with dynamic boundary conditions. Math Z, 1992, 210: 413-439
[25] Fabes E B, Kenig C E, Serapioni R P. The local regularity of solutions of degenerate elliptic equations. Comm Partial Differential Equations, 1982, 7(1): 77-116
[26] Fang F, Tan Z. Heat flow for Dirichlet-to-Neumann operator with critical growth. Adv Math, 2018, 328: 217-247
[27] Fila M, Ishige K, Kawakami T. Convergence to the Poisson kernel for the Laplace equation with a nonlinear dynamical boundary condition. Comm Pure Appl Math, 2012, 11(3): 1285-1301
[28] Fila M, Quittner P. Global solutions of the Laplace equation with a nonlinear dynamical boundary condition. Math Methods Appl Sci, 1997, 20: 1325-1333
[29] Fino A, Karch G. Decay of mass for nonlinear equations with fractional Laplacian. Monatshefte fÜr Mathmatik,2010, 160(4): 375-384
[30] Fujita H. On the blowing up of solutions of the Cauchy problem for $u_t = \Delta u + u^{1+\alpha}$. J Fac Sci Univ Tokyo, 1966, 13: 109-124
[31] Giga Y. A bound for global solutions of semilinear heat equations. Comm Math Phys, 1986, 103: 415-421
[32] Guedda M, Kirane M. A note on nonexistence of global solutions to a nonlinear integral equation. Bull Belg Math Soc Simon Stevin, 1999, 6(4): 491-497
[33] Hintermann T. Evolution equation with dynamic boundary conditions. Proc Roy Soc Edinburgh Sect A, 1989, 135: 43-60
[34] Ishii H. Asymptotic stability and blowing up of solutions of some nonlinear equations. J Differential Equations, 1977, 26(2): 291-319
[35] Kirane M. Blow-up for some equations with semilinear dynamical boundary conditions of parabolic and hyperbolic type. Hokkaido Math J, 1992, 21: 221-229
[36] Koleva M. On the computation of blow-up solutions of elliptic equations with semilinear dynamical boundary conditions. Lect Notes Comput Sci, 2004, 2907: 473-480
[37] Koleva M, Vulkov L. Blow-up of continuous and semidiscrete solutions to elliptic equations with semilinear dynamical boundary conditions of parabolic type. J Comput Appl Math, 2007, 202: 414-434
[38] LadyŽenskaja O A, Solonnikov V A, Ural'ceva N N. Linear and Quasilinear Equations of Parabolic Type. Providence RI: American Mathematical Society, 1968
[39] Leseduarte M C, Quintanilla R. Phragmén-Lindelöf alternative for the Laplace equation with dynamic boundary conditions. J Appl Anal Comput,2017, 7(4): 1323-1335
[40] Lions J L.Quelques Méthodes de Résolutions des Problémes aux Limites Non Linéaires (French). Paris: Dunod, 1969: 134-140
[41] Meyries M.Maximal Regularity in Weighted Spaces, Nonlinear Boundary Conditions, and Global Attractors[D]. Karlsruhe: Karlsruher Institut fÜr Technologie, 2001
[42] Musso M, Sire Y, Wei J, Zhou Y. Infinite time blow-up for the fractional heat equation with critical exponent. Math Ann, 2019, 375(1/2): 361-424
[43] Ni W M, Sacks P E, Tavantzis J. On the asymptotic behavior of solutions of certain quasilinear equations of parabolic type. J Differential Equations, 1984, 54: 97-120
[44] Payne L E, Sattinger D H. Saddle points and instability of nonlinear hyperbolic equations. Israel J Math, 1975, 22(3/4): 273-303
[45] Servadei R, Valdinoci E. The Brezis-Nirenberg result for the fractional Laplacian. Trans Amer Math Soc, 2015, 367: 67-102
[46] Sugitani S. On nonexistence of global solutions for some nonlinear integral equations. Osaka J Math, 1975, 12: 45-51
[47] Tan J G. Positive solutions for non local elliptic problems. Discrete Contin Dyn Syst, 2013, 33(2): 837-859
[48] Tan Z. Global solution and blow-up of semilinear heat equation with critical Sobolev exponent. Comm Partial Differential Equations, 2001, 26: 717-741
[49] Touzani R, Rappaz J.Mathematical Models for Eddy Currents and Magnetostatics. Heidelberg: Springer, 2014
[50] Uhlmann G. Topical review: electrical impedance tomography and Calderón's problem. Inverse Problems,2009, 25: 123011
[51] Vitillaro E. On the Laplace equation with non-linear dynamical boundary conditions. Proc London Math Soc, 2006 93(2): 418-446
[52] Warma M. On a fractional (s, p)-Dirichlet-to-Neumann operator on bounded Lipschitz domains. J Ellipt Parab Equ, 2018, 4(8): 223-269
[53] Weissler F B. Local existence and nonexistence for semilinear parabolic equation in $L^p$. Indiana Uni Math J, 1980, 29(1): 79-102
[54] Yin Z. Global existence for elliptic equations with dynamic boundary conditions. Arch Math, 2003, 81(5): 567-574
[55] Zhang T T, Jang G Y, Oh T I, et al. Source consistency electrical impedance tomography. SIAM J Appl Math, 2020, 80(1): 499-520
[56] Zhou L, Harrach B, Seo J K. Monotonicity-based electrical impedance tomography for lung imaging. Inverse Problem, 2018, 34(4): 045005
