Quenching of the solution to the discrete heat equation with logarithmic type sources on graphs. (English) Zbl 1477.39001
The authors study the discrete heat equation with logarithmic type sources on graphs. Both local existence and uniqueness of solutions are proved, and the quenching behavior of solutions and the blow-up of their time-derivatives are studied. Further, the critical exponent for the global existence and the quenching of the solutions is obtained.
Reviewer: Cheng He (Beijing)
MSC:
| 39A14 | Partial difference equations |
| 39A12 | Discrete version of topics in analysis |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35K55 | Nonlinear parabolic equations |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35K05 | Heat equation |
| 35R02 | PDEs on graphs and networks (ramified or polygonal spaces) |
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