Conditions for the Transformation of a Diffusion Wave into a Traveling Wave within the System of Burgers-type Equations

We study the new effect of the transition from N-wave to traveling wave behavior of the solution to the system of two Burgers-type equations arising from the study of the Schumpeterian dynamics of innovations. We explain the conditions under which the soliton-like propagating traveling-wave captures...

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Bibliographic Details
Published inLobachevskii journal of mathematics Vol. 46; no. 1; pp. 190 - 201
Main Author Egorov, L. V.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.01.2025
Springer Nature B.V
Subjects
Algebra
Analysis
Burgers equation
Diffusion waves
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Shock waves
Solitary waves
Traveling waves
diffusion wave
shock wave
entropy solution
coupled Burgers-type equations
traveling-wave solution
2010 Mathematics Subject Classification: 35C07, 35Q35, 93A30
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ISSN1995-0802
1818-9962
DOI10.1134/S1995080224608464

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Summary:We study the new effect of the transition from N-wave to traveling wave behavior of the solution to the system of two Burgers-type equations arising from the study of the Schumpeterian dynamics of innovations. We explain the conditions under which the soliton-like propagating traveling-wave captures the diffusion wave and forms another traveling-wave (shock wave in the inviscid case). A method for determining the exact value of the propagation speed of the emerging evolutionary dynamics is described.
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ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080224608464