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.
CITATION STYLE
Lukyanenko, D., & Nefedov, N. (2019). Blow-Up of Fronts in Burgers Equation with Nonlinear Amplification: Asymptotics and Numerical Diagnostics. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11386 LNCS, pp. 72–79). Springer Verlag. https://doi.org/10.1007/978-3-030-11539-5_7
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