Recovering the initial distribution for a logarithmic nonlinear biparabolic equation

Abstract

In this paper, we consider the problem of finding the initial distribution for a biparabolic equation with logarithmic nonlinearity source. The problem is severely ill‐posed in the sense of Hadamard. Under the a priori assumption on the exact solution belonging to a Gevrey space, we consider a generalized nonlinear problem by using the Fourier truncation method to obtain rigorous convergence estimates in the norms on Lq space with some q ≥ 2 and the Sobolev space Ws, ℓ for some constants s > 0, ℓ ≥ 1.