Global solvability for quasilinear parabolic equation with inhomogeneous density and a source |
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| Authors: | A.V. Martynenko |
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| Affiliation: | 1. Department of Mathematical Analysis and Algebra, Institute of Information Technologies , Luhansk Taras Shevchenko National University , Luhansk , Ukraine amartynenko@rambler.ru |
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| Abstract: | We study the Cauchy problem for quasilinear parabolic equation with inhomogeneous density and a source. We show that this problem has a global solution under the assumptions that initial datum is small enough in the integral sense and the source term has overcritical behaviour. The sharp estimates of a solution is obtained as well. |
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| Keywords: | quasilinear parabolic equation inhomogeneous density Fujita critical exponent global existence |
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