Nguyen Anh TrietBaleanu, DumitruO'Regan, DonalBaleanu, DumitruNguyen Hoang LucNguyen CanMatematik2020-04-282020-04-282020Anh Triet N...et al. (2020). "A Filter Method for Inverse Nonlinear Sideways Heat Equation", Advances In Difference Equations, Vol. 20, No. 1.1687-1847https://doi.org/10.1186/s13662-020-02601-4In this paper, we study a sideways heat equation with a nonlinear source in a bounded domain, in which the Cauchy data at x=X are given and the solution in 0 <= x < X is sought. The problem is severely ill-posed in the sense of Hadamard. Based on the fundamental solution to the sideways heat equation, we propose to solve this problem by the filter method of degree alpha, which generates a well-posed integral equation. Moreover, we show that its solution converges to the exact solution uniformly and strongly in L-p(omega,X; L-2 (R)); omega is an element of[0,X) under a priori assumptions on the exact solution. The proposed regularized method is illustrated by numerical results in the final section.eninfo:eu-repo/semantics/openAccessBackward ProblemNonlinear Heat EquationIll-Posed ProblemCauchy ProblemRegularization MethodError EstimateArticle2020110.1186/s13662-020-02601-42-s2.0-85083068713WOS:000526565300002Q1N/A