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Hyers-Ulam Stability of a multivariate partial differential equation

Yongjin Li and Jinghao Huang

We prove the Hyers-Ulam stability of a partial differential equation. That is, if u is an approximate solution of Pn i=1 aiuxi (x1, x2, · · · , xn) + g(xj )u(x1, x2, · · · , xn) + h(xj ) = 0, then there exists an exact solution of the differential equation near to u