Fujita-type theorems for doubly degenerate parabolic equations with a time-weighted source. (English) Zbl 1338.35032
Summary: This work deals with the Cauchy problem for a doubly degenerate parabolic equation with a time-weighted source. Existence and non-existence results for global solutions of this problem are established. Sharp estimates of the solution are obtained in the case of global solvability.
MSC:
| 35B33 | Critical exponents in context of PDEs |
| 35B45 | A priori estimates in context of PDEs |
| 35K65 | Degenerate parabolic equations |
| 35B44 | Blow-up in context of PDEs |
| 35K59 | Quasilinear parabolic equations |
References:
| [1] | Fujita H, J. Fac. Sci. Univ. Tokyo Sect. I 13 pp 109– (1966) |
| [2] | Galaktionov VA, Dokl. Akad. Nauk SSSR 252 pp 1362– (1980) |
| [3] | Andreucci D, Ann. Sc. Normale Sup. Pisa 18 pp 363– (1991) |
| [4] | DOI: 10.1016/0041-5553(82)90037-4 · Zbl 0548.35068 · doi:10.1016/0041-5553(82)90037-4 |
| [5] | DOI: 10.1006/jdeq.1995.1132 · Zbl 0836.35081 · doi:10.1006/jdeq.1995.1132 |
| [6] | DOI: 10.1016/S0362-546X(97)00716-5 · Zbl 1139.35317 · doi:10.1016/S0362-546X(97)00716-5 |
| [7] | DOI: 10.1006/jmaa.1998.6253 · Zbl 0920.35079 · doi:10.1006/jmaa.1998.6253 |
| [8] | Samarskii AA, Blow-up in quasilinear parabolic equations. Nauka, Moscow, 1987 (1985) |
| [9] | DOI: 10.1137/1032046 · Zbl 0706.35008 · doi:10.1137/1032046 |
| [10] | DOI: 10.1006/jmaa.1999.6663 · Zbl 0942.35025 · doi:10.1006/jmaa.1999.6663 |
| [11] | DOI: 10.1017/S0308210500027190 · Zbl 0892.35088 · doi:10.1017/S0308210500027190 |
| [12] | DOI: 10.1006/jmaa.2001.7771 · Zbl 1010.35005 · doi:10.1006/jmaa.2001.7771 |
| [13] | DOI: 10.1006/jmaa.2000.7341 · Zbl 0984.35020 · doi:10.1006/jmaa.2000.7341 |
| [14] | DOI: 10.1080/00036811.2013.794937 · Zbl 1288.35055 · doi:10.1080/00036811.2013.794937 |
| [15] | DOI: 10.1006/jmaa.2001.7553 · Zbl 0993.35057 · doi:10.1006/jmaa.2001.7553 |
| [16] | DOI: 10.1134/S0965542508070087 · doi:10.1134/S0965542508070087 |
| [17] | DOI: 10.1016/j.na.2010.06.026 · Zbl 1195.35068 · doi:10.1016/j.na.2010.06.026 |
| [18] | DOI: 10.1007/BF01456275 · Zbl 0609.35048 · doi:10.1007/BF01456275 |
| [19] | DOI: 10.1007/BF01176474 · Zbl 0497.35049 · doi:10.1007/BF01176474 |
| [20] | DOI: 10.1016/0022-247X(88)90053-4 · Zbl 0681.35047 · doi:10.1016/0022-247X(88)90053-4 |
| [21] | DOI: 10.1007/BF02567072 · Zbl 0755.35053 · doi:10.1007/BF02567072 |
| [22] | DOI: 10.1007/s10114-004-0375-6 · Zbl 1073.35130 · doi:10.1007/s10114-004-0375-6 |
| [23] | DOI: 10.1080/00036810701435711 · Zbl 1129.35044 · doi:10.1080/00036810701435711 |
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