References
- [1] B. Abdellaoui, R. Benteffour , Caarelli-Kohn-Nirenbgerg type inequalities of fractional order and applications. Journal of Functional Analysis. 272 (2017), no. 10, 3998-4029.
- [2] B. Abdellaoui, M. Medina, I. Peral, A. Primo Optimal results for the fractional heat equation involving the Hardy potential . Nonl. Anal. TMA. 140 (2016), 166-207.
- [3] R. A. Adams Sobolev spaces, Academic Press, New York, 1975.
- [4] B. Baeumer, S. Kurita, M.M. Meerschaert Inhomogeneous fractional diffusion equations. Fractional Calculus and Applied Analysis 8(4), 371-386.
- [5] H. Bei Blow-up theories for semilinear parabolic equations. Lecture notes in mathematics, 2018.
- [6] A. Boucherif Nonlocal problems for parabolic inclusions. 7th AIMS Conference, Dynamical systems, differential equations and applications. Discrete Contin. Dyn. Syst. 2009, suppl. 82-91.
- [7] A. Boucherif Semilinear evolution inclusions with nonlocal conditions. Appl. Math. Lett. 22 (2009), no. 8, 1145-1149.10.1016/j.aml.2008.10.004
- [8] J. R. Cannon The solution of the heat equation subject to the specification of energy, Quart. Appl. Math. 21 (1963), 155-160.10.1090/qam/160437
- [9] R. Yu Chegis Numerical solution of a heat conduction problem with an integral boundary condition, Litovsk. Mat. Sb. 24 (1984), 209-215.
- [10] D.H. Dai and Yu Huang Remarks on a semilinear heat equation with integral boundary conditions, Nonl. Anal. 67 (2007), 468-475.10.1016/j.na.2006.06.012
- [11] W. A. Day A decreasing property of solutions of parabolic equations with applicatons to thermoelasticity, Quart. Appl. Math. 41 (1983), 468-475.10.1090/qam/693879
- [12] M. Dehghan Efficient techniques for the second order parabolic equation subject to nonlocal specifications, Appl. Numer. Math. 52 (2005), 39-62.10.1016/j.apnum.2004.02.002
- [13] K. Deng Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions, J. Math. Anal. Appl. 179 (1993), 630-637.10.1006/jmaa.1993.1373
- [14] E. Di Nezza, G. Palatucci, E. Valdinoci Hitchhiker's guide to the fractional Sobolev spaces, Bull. Sci. math. 136 (2012), no. 5, 521-573.
- [15] M. Felsinger, M. Kassmann, Local regularity for parabolic nonlocal operators. Comm. PDE, 38 (2013) 1539{1573.
- [16] A. Gladkov, M. Guedda Blow-up problem for semilinear heat equation with absorption and a nonlocal boundary condition, Nonl. Anal. TMA. 74 (2011), 4573-4580.10.1016/j.na.2011.04.027
- [17] N. Ionkin and E. MoiceevSolution of boundary value problem in heat conduction theory with nonlocal boundary conditions, Differential Equations (1977), 294-304, 1977.
- [18] T. Leonori, I. Peral, A. Primo, F. Soria Basic estimates for solutions of a class of nonlocal elliptic and parabolic equations. Discrete and Continuous Dynamical Systems, 35 (2015)10.3934/dcds.2015.35.6031
- [19] J. L. Lions Quelques methodes de resolution des problemes aux limites nonlineaires Edition Dunod, Paris 1969.
- [20] W. E. Olmstead and C. A. Roberts The one dimensional heat equation with a nonlocal initial condition, Appl. Math. Lett. 10 (1997), 89-94.10.1016/S0893-9659(97)00041-4
- [21] H-M. Yin On a class of parabolic equations with nonlocal boundary conditions, J. Math. Anal. Appl. 294 (2004), 712-728.10.1016/j.jmaa.2004.03.021