JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (10): 41-47.doi: 10.6040/j.issn.1671-9352.0.2015.613

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Cauchy problem for nonlinear parabolic equation systems with initial data measures

SONG Meng-meng, SHANG Hai-feng   

  1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, Henan, China
  • Received:2015-12-17 Online:2016-10-20 Published:2016-10-17

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Abstract: The Cauchy problem for a class of degenerate parabolic system with strongly coupling source is studied, where initial data are measured. When the known parameters satisfy some conditions, the difficulties are avoided which come from the interactions between the degeneracy of the principal and the strongly coupling source, and the existence of solutions is obtained. Moreover, it is proved that these conditions are optimal for the existence of solutions.

Key words: parabolic equation system, Cauchy problem, measures as initial data, coupling nonlinear source

CLC Number: 

  • O175.2
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