Abstract
In this paper, we study the global solvability of well-known equations used to describe nonlinear processes with dissipation, namely, the Burgers equation, the Korteweg–de Vries–Burgers equation, and the modified Korteweg–de Vries–Burgers equation. Using a method due to Pokhozhaev, we obtain necessary conditions for the blow-up of global solutions and estimates of the blow-up time and blow-up rate in bounded and unbounded domains. We also study the effect of linear and nonlinear viscosity on the occurrence of a gradient catastrophe in finite time.
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Original Russian Text © E. V. Yushkov, M. O. Korpusov, 2015, published in Matematicheskie Zametki, 2015, Vol. 98, No. 3, pp. 448–462.
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Yushkov, E.V., Korpusov, M.O. Global unsolvability of one-dimensional problems for Burgers-type equations. Math Notes 98, 503–514 (2015). https://doi.org/10.1134/S0001434615090163
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DOI: https://doi.org/10.1134/S0001434615090163