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Approximate solution for a variable-coefficient semilinear heat equation with nonlocal boundary conditions. (English) Zbl 1182.35143
Summary: This paper develops an iterative algorithm for the solution to a variable-coefficient semilinear heat equation with nonlocal boundary conditions in the reproducing space. It is proved that the approximate sequence $u_n(x, t)$ converges to the exact solution $u(x, t)$. Moreover, the partial derivatives of $u_n(x, t)$ are also convergent to the partial derivatives of $u$(x, t). And the approximate sequence $u_n(x, t)$ is the best approximation under a complete normal orthogonal system.

35K58Semilinear parabolic equations
35A35Theoretical approximation to solutions of PDE
35K20Second order parabolic equations, initial boundary value problems
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