S. B. de Menezes, "Remarks on weak solutions for a nonlocal parabolic problem", International Journal of Mathematics and Mathematical Sciences, vol. 2006, Article ID 082654, 10 pages, 2006. https://doi.org/10.1155/IJMMS/2006/82654
Remarks on weak solutions for a nonlocal parabolic problem
We prove a result on existence and uniqueness of weak solutions for a diffusion problem associated with nonlinear diffusions of nonlocal type studied by Chipot and Lovat (1999) by an application of the fixed point result of Schauder. Moreover, making use of Faedo-Galerkin approximation, coupled with some technical ideas, we establish a result on existence of periodic solution.
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