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Local solvability and blowup of the solution of the Rosenau-Bürgers equation with different boundary conditions

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Abstract

We consider several models of initial boundary-value problems for the Rosenau-Bürgers equation with different boundary conditions. For each of the problems, we prove the unique local solvability in the classical sense, obtain a sufficient condition for the blowup regime, and estimate the time of the solution decay. The proof is based on the well-known test-function method.

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Author information

Correspondence to A. A. Panin.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 177, No. 1, pp. 93–110, October, 2013.

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Panin, A.A. Local solvability and blowup of the solution of the Rosenau-Bürgers equation with different boundary conditions. Theor Math Phys 177, 1361–1376 (2013). https://doi.org/10.1007/s11232-013-0109-y

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Keywords

  • blowup regime
  • local solvability
  • noncontinuable solution
  • Rosenau-Bürgers equation