The asymptotic behavior of the wave and heatconduction equations in twodimensional exterior spaces
Abstract
The timeasymptotic behavior of the initialvalue and boundaryvalue problems of wave and heatconduction equations with timeindependent righthand terms (f) is investigated analytically for the twodimensional space outside a closed curve, considering both Neumann boundary conditions and the corresponding Dirichlet problems and applying a spectraltheory approach. The solutions for the Neumann case are found to increase logarithmically as t goes to infinity as long as the integral of f dx is not equal to zero; in the Dirichlet case, the solutions converge to the solution of the corresponding static problem. The results for the wave equation are shown to be identical with those obtained by Muravei (1978) by a different method.
 Publication:

Mathematical Methods in the Applied Sciences
 Pub Date:
 1985
 DOI:
 10.1002/mma.1670070111
 Bibcode:
 1985MMAS....7..170W
 Keywords:

 Boundary Value Problems;
 Conductive Heat Transfer;
 Wave Equations;
 Asymptotic Properties;
 Boundary Conditions;
 Dirichlet Problem;
 Neumann Problem;
 Fluid Mechanics and Heat Transfer