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The Nonlinear Heat Equation on W-Random Graphs
For systems of coupled differential equations on a sequence of W -random graphs, we derive the continuum limit in the form of an evolution integral equation. We prove that solutions of the initial value problems (IVPs) for the discrete model converge to the solution of the IVP for its continuum limi...
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| Published in: | Archive for rational mechanics and analysis 2014-06, Vol.212 (3), p.781-803 |
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| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c415t-24213ae9505e97b4ca822887a8074e90504d2f62c835d5e921ae9f9463a80f973 |
| container_end_page | 803 |
| container_issue | 3 |
| container_start_page | 781 |
| container_title | Archive for rational mechanics and analysis |
| container_volume | 212 |
| creator | Medvedev, Georgi S. |
| description | For systems of coupled differential equations on a sequence of
W
-random graphs, we derive the continuum limit in the form of an evolution integral equation. We prove that solutions of the initial value problems (IVPs) for the discrete model converge to the solution of the IVP for its continuum limit. These results combined with the analysis of nonlocally coupled deterministic networks in Medvedev (The nonlinear heat equation on dense graphs and graph limits. ArXiv e-prints,
2013
) justify the continuum (thermodynamic) limit for a large class of coupled dynamical systems on convergent families of graphs. |
| doi_str_mv | 10.1007/s00205-013-0706-9 |
| format | article |
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2013
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2013
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2013
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| ispartof | Archive for rational mechanics and analysis, 2014-06, Vol.212 (3), p.781-803 |
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| language | eng |
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| source | Springer Link |
| subjects | Classical Mechanics Complex Systems Continuums Differential equations Evolution Fluid- and Aerodynamics Graphs Heat equations Initial value problems Mathematical and Computational Physics Mathematical models Nonlinearity Physics Physics and Astronomy Theoretical |
| title | The Nonlinear Heat Equation on W-Random Graphs |
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