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Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations
Qiao Zhu, Dmitrii Chaikovskii, Bangti Jin +1
Physics-informed neural network (PINN) has shown great potential in solving partial differential equations. However, it faces challenges when dealing with problems involving steep…
Internal layer solutions and coefficient recovery in time-periodic reaction-diffusion-advection equations
Dmitrii Chaikovskii, Ye Zhang, Aleksei Liubavin
This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a non…
Asymptotic expansion regularization for inverse source problems in two-dimensional singularly perturbed nonlinear parabolic PDEs
Dmitrii Chaikovskii, Aleksei Liubavin, Ye Zhang
In this paper, we develop an asymptotic expansion-regularization (AER) method for inverse source problems in two-dimensional nonlinear and nonstationary singularly perturbed partia…