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 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.