On the Solution of Triharmonic Bessel Heat Equation

Wanchak Satsanit

Abstract

AbstractIn this paper, we study the equation@@tu(x; t) = c2 ­kB u(x; t)with the initial condition u(x; 0) = f(x) for x 2 R+n : The operator ­kB is the operatoriterated k¡ times and de¯ned by­kB =0@ÃXpi=1Bxi!3¡ÃXp+qj=p+1Bxi!31Ak;where p+q = n is the dimension of the R+n; Bxi = @2@x2i+ 2vixi@@xi;, 2vi = 2®i+1 ; ®i > ¡12i = 1; 2; 3; :::; n; and k is a nonnegative integer, u(x; t) is an unknown function for(x; t) = (x1; x2; : : : ; xn; t) 2 R+n £(0;1), f(x) is a given generalized function and c is apositive constant. By the Fourier transform in sense of Distribution theory we obtainthe solution of such equation and related to the triharmonic Besel heat equation.