## 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.

### MSC:

 35K58 Semilinear parabolic equations 35A35 Theoretical approximation in context of PDEs 35K20 Initial-boundary value problems for second-order parabolic equations
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### References:

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