On a nonlocal problem for nonlinear pseudoparabolic equations |
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Authors: | Dao-Qing Dai Yu Huang |
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Affiliation: | Department of Mathematics, Sun Yat-Sen (Zhongshan) University, Guangzhou 510275, PR China |
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Abstract: | For a nonlinear pseudoparabolic equation with one space dimension we consider its initial boundary value problem on an interval. The boundary condition on the left end is of Dirichlet type, the right end condition is replaced by a nonlocal one. Because it is given by an integral, the function involved could exhibit singularities, which distinguishes this nonlocal condition from its Dirichlet counterpart. Based on an elliptic estimate and an iteration method we established the well-posedness of solutions in a weighted Sobolev space. |
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Keywords: | Nonlinear pseudoparabolic equation Weighted Sobolev space Elliptic estimate Nonlocal boundary condition |
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