Title of article :
On the solutions of the Cauchy problem for a class of partial differential equations with double characteristic at a point
Author/Authors :
Ali Bentrad، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2011
Pages :
16
From page :
3652
To page :
3667
Abstract :
We give an explicit representation of the solutions of the Cauchy problem, in terms of series of hypergeometric functions, for the following class of partial differential equations with double characteristic at the origin:(xk∂t+a∂x)(xk∂t+b∂x)u+cxk−1∂tu=0,u(0,x)=u0(x),∂tu(0,x)=u1(x). We show that the solutions are holomorphic, ramified around the characteristic surfaces K=K1 K2 K3 with K3:x=0.
Keywords :
Singular solutionsHypergeometric equation
Journal title :
JOURNAL OF DIFFERENTIAL EQUATIONS
Serial Year :
2011
Journal title :
JOURNAL OF DIFFERENTIAL EQUATIONS
Record number :
752045
Link To Document :
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