Heat equation for a general convex domain in R³ with a finite number of piecewise impedance boundary conditions

Abstract

The spectral function , where are are the eigenvalues of the negative Laplacian –space, is studied for agiven arbitrary simply connected bounded domain together with a finite number of piecewise smooth impedance boundary conditions on the parts S_i (i≡l,…,m) of its bounding surface S such that .

Keywords:

• Inverse eigenvalue problem
• spectral functions

AMS(MOS)::

• 35K
• 35P

^*Present address: mathematics department, Faculty of Science, University of Emirates, P.O. Box 15551, Al-Ain United Arab Emirates.

^*Present address: mathematics department, Faculty of Science, University of Emirates, P.O. Box 15551, Al-Ain United Arab Emirates.

Notes

^*Present address: mathematics department, Faculty of Science, University of Emirates, P.O. Box 15551, Al-Ain United Arab Emirates.