A transient solution on potential equation of diffusion type with time-varying coefficients

Abstract

Research on hydrothermal sulphide ore of marine mineral resources exploration is hot recently. According to the general solution of first order differential equation, Laplace transform is used to transform the linear homogeneous differential equation of second order variable coefficient into first order differential equation of complex domain. The general solution of the first-order differential equations in complex domain is similarly obtained without regard for the difference between real domains and complex domains. Further more, the general solutions are deduced to the second order linear differential equations with variable coefficients. Then it is used to solve the thermoelectric coupling electric field model in oceanic strike exploration; A closed analytical solution with integral form of elementary functions is obtained to the simplified diffusion electric field potential model. To get an explicit solution, with the help of MAPLE software, the general solution of the linear combination of Kummer functions is obtained. This research has theoretical significance for the engineering implementation of the frequency domain induced dipole drag system.