2020 / March Volume 15 No.1
Solvability and Blow-up of Solutions of Semi Linear Parabolic Problem with Integral Condition of Second Type
| Published Date |
2020 / March
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| Title | Solvability and Blow-up of Solutions of Semi Linear Parabolic Problem with Integral Condition of Second Type |
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| Pagination | 33-52 |
| Abstract | In this paper, semi-linear parabolic equation with integral boundary condition of second type is investigated. The existence, uniqueness and Blow-up of weak solutions in finite time are established. The proof is proceeds in two steps; using the variable separation method for the solvability of the linear cas and applying an iterative process
and a priori estimate, we prove the existence, uniqueness of the weak solution of the semi-linear problem. Finally, we study a blow-up of solution in finite time for a super-linear problem by using eigen functions method introduced by Kaplan.
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| DOI | |
| AMS Subject Classification |
35K55, 35K61, 35B44, 35B45, 35A01, 35A02
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| Received |
2020-01-21
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