https://orcid.org/0000-0002-1867-034X
References
- E. Bendito, A. Carmona and A.M. Encinas, Boundary value problems on weighted networks, Discrete Appl. Math. 156(18) (2008), pp. 3443–3463. doi: 10.1016/j.dam.2008.02.008
- A. Carmona, A.M. Encinas and M. Mitjana, Eigenvalues with respect to a weight for general boundary value problems on networks, Linear Algebra Appl. (2020). In press. Available at https://doi.org/10.1016/j.laa.2020.03.046.
- R. Castillo and M. Loayza, On the critical exponent for some semilinear reaction-diffusion systems on general domains, J. Math. Anal. Appl. 428(2) (2015), pp. 1117–1134. doi: 10.1016/j.jmaa.2015.03.035
- F.R.K. Chung, Spectral Graph Theory, CBMS Regional Conference Series in Math. 92, Amer. Math. Soc., USA, 1997.
- S.-Y. Chung and C.A. Berenstein, ω-harmonic functions and inverse conductivity problems on network, SIAM J. Appl. Math. 65 (2005), pp. 1200–1226. doi: 10.1137/S0036139903432743
- S.-Y. Chung and J. Hwang, A complete characterization of the discrete p-Laplacian parabolic equations with q-nonlocal reaction with respect to the blow-up property, J. Math. Anal. Appl. 473(2) (2019), pp. 1447–1473. doi: 10.1016/j.jmaa.2019.01.031
- S.-Y. Chung and J. Hwang, The discrete p-Schrödinger equations under the mixed boundary conditions on networks, Physica D 395 (2019), pp. 43–59. doi: 10.1016/j.physd.2019.02.009
- S.-Y. Chung, M.-J. Choi and J.-H. Park, Fujita-type blow-up for discrete reaction-diffusion equations on networks, Publ. Res. Inst. Math. Sci. 55 (2019), pp. 235–258. doi: 10.4171/PRIMS/55-2-1
- S.-Y. Chung, M.-J. Choi and J.-H. Park, On the critical set for Fujita type blow-up of solutions to the discrete Laplacian parabolic equations with nonlinear source on networks, Comput. Math. Appl.78(6) (2019), pp. 1838–1850. doi: 10.1016/j.camwa.2019.02.016
- D.M. Cvetkovic, M. Doob and H. Sachs, Spectra of Graphs: Theory and Applications, Acad. Press, New York, 1980.
- J. Ding, Global and blow-up solutions for nonlinear parabolic equations with Robin boundary conditions, Comput. Math. Appl. 65(11) (2013), pp. 1808–1822. doi: 10.1016/j.camwa.2013.03.013
- C. Enache, Blow-up phenomena for a class of quasilinear parabolic problems under Robin boundary condition, Appl. Math. Lett. 24(3) (2011), pp. 288–292. doi: 10.1016/j.aml.2010.10.006
- H. Fujita, On the blowing up of solutions of the Cauchy problem for ut=Δu+u1+α, J. Fac. Sci. Univ. Tokyo Sect. I 13 (1966), pp. 109–124.
- P. Meier, On the critical exponent for reaction-diffusion equations, Arch. Rational Mech. Anal. 109(1) (1990), pp. 63–71. doi: 10.1007/BF00377979
- J. Poland and D.R. Kassoy, The induction period of a thermal explosion in a gas between infinite parallel plates, Combust. Flame 50 (1983), pp. 259–274. doi: 10.1016/0010-2180(83)90069-X
- P. Souplet, Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source, J. Differ. Equ. 153(2) (1999), pp. 374–406. doi: 10.1006/jdeq.1998.3535
- W. Zhou, M. Chen and W. Liu, Critical exponent and blow-up rate for the ω-diffusion equations on graphs with Dirichlet boundary conditions, Electron. J. Differ. Equ. 2014(263) (2014), 13 pp.