On a singular two dimensional nonlinear evolution equation with nonlocal conditions |
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Authors: | Said Mesloub |
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Institution: | King Saud University, College of Sciences, Department of Mathematics, P.O. Box 2455, Riyadh 11451, Saudi Arabia |
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Abstract: | This paper deals with a nonclassical initial boundary value problem for a two dimensional parabolic equation with Bessel operator. We prove the existence and uniqueness of the weak solution of the given nonlinear problem. We start by solving the associated linear problem. After writing this latter in its operator form, we establish an a priori bound from which we deduce the uniqueness of the strong solution. For the solvability of the associated linear problem, we prove that the range of the operator generated by the considered problem is dense. On the basis of the obtained results of the linear problem, we apply an iterative process to establish the existence and uniqueness of the nonlinear problem. |
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Keywords: | 35K 35R |
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