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摘要
Stefan phase change model is a second order partial differential equation (or set) in thermal dissociation natural gas hydrate. The demonstration of existence and uniqueness, and the probe of Laplace method of the solution to Stefan phase change model were discussed for the thermal dissociation natural gas hydrate. The simplification process and the detailed derivation for the model were deduced. By using the iterative scheme method of differential equations, the maximum and minimum lemma and the range of parameter values were derived. The proof of the existence of the limit of xn(t), Tn(x, t) by alternating condition maps on the boundary confirms the existence of the solution of the differential equation. The uniqueness of the solution of Stefan differential equation is proved by contradictory method. Using Laplace transform, separation of variables and Laplace inverse transform method, the analytical solution of the Stefan model is obtained, and the monotonicity proof of the transcendental equation verifies the uniqueness of the solution of the equation. ? 2023 Materials China.
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