Abstract
This work develops a theory of asymptotic-numerical investigations of moving fronts in reaction-diffusion-advection models. We present the result of consideration of singularly perturbed parabolic Burgers-type equations with nonlinear forcing. Conditions of solution blow-up are formulated. Numerical algorithm which allows to recognise and describe the solutions blow-up is presented. In particular, in order to demonstrate the proposed method, we apply our approach to the problem with cubic forcing.
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The work was supported by the Russian Science Foundation [grant number 18-11-00042].
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Lukyanenko, D., Nefedov, N. (2019). Blow-Up of Fronts in Burgers Equation with Nonlinear Amplification: Asymptotics and Numerical Diagnostics. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science(), vol 11386. Springer, Cham. https://doi.org/10.1007/978-3-030-11539-5_7
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