RMC - Vol. 8, Num. 2 - E. Bisognin

Full paper in PDF:
$%E. Bisognin, Hyperbolic parabolic equations with nonlinearity of Kirchoff-Carrier type, Rev. Mat. Univ. Complut. Madrid 8 (1995), no. 2, 401–430.%$

Hyperbolic Parabolic Equations with Nonlinearity of Kirchoff-Carrier Type

Eleni BISOGNIN

Department of Mathematics
Federal University of Santa Maria
97119-900 Santamaria — Brazil

eleni@brufsm.bitnet

Received: September 9, 1993
Revised: August 19, 1994

ABSTRACT

In this work we study the existence of local solutions for the Cauchy problem of the hyperbolic-parabolic equation

1 (K1u')'+K2u'+ Au + M(t,| A 2u|2)Au =f.

(*)

We represent by $A$ a self-adjoint, positive linear operator of a Hilbert space, $M$ is a real $C1$ -function with time dependence, such that $M(t,j)> 0$ for all $(t,j) (- [0,T]× [0, oo [$ and $K1$ , $K2$ are real functions defined on $[0,T]$ satisfying the conditions, $K1(t)> 0$ and $K2(t)> d0 > 0$ .

The existence of local solution for (*) is proved by Diagonalization Theorem.

1991 Mathematics Subject Classification: 35K45, 35L15.