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S Tiwari, S Engu, Manas Ranjan Sahoo, On solutions to the Cauchy problem for a class of forced Burgers equations, The Quarterly Journal of Mechanics and Applied Mathematics, Volume 77, Issue 3, August 2024, hbae011, https://doi.org/10.1093/qjmam/hbae011
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Summary
A Cauchy problem for forced Burgers equation (FBE) with time-dependent coefficients is studied in this work. We find explicit solutions of the FBE in terms of Hermite polynomials subject to various classes of initial data. Further, we prove the existence of solutions of FBE with respect to the bounded, continuous and summable initial data. We then derive an approximate solution to the Cauchy problem and find the error estimations between the true and approximate solutions. We give asymptotic profiles of the solutions depending on the initial data.