J4 ›› 2013, Vol. 48 ›› Issue (8): 50-55.

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Cauchy problem for doubly nonlinear parabolic equations with time-dependent source

CHENG Jun-xiang, SHANG Hai-feng   

  1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo  454000,  Henan,  China
  • Received:2012-12-24 Online:2013-08-20 Published:2013-08-21

Abstract:

The Cauchy problem of the equation ut-div(|Dum|p-2Dum)=t-σuq,is studied, where m>0, p>1. This equation is called doubly nonlinear parabolic equation, since the principal part may be doubly degenerate or doubly singular related to the parameters m, p. By a priori estimates and compactness methods, and fine classifications to parameters m, p, we obtain the optimal existence of solutions of the equation with initial data measures are obtained.

Key words: Cauchy problem; doubly nonlinear equation; time-dependent source; measures as initial data

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