Exact estimates of the amplitude and support of unbounded solutions of the nonlinear heat equation with a source
Abstract
Exact upperbound estimates of the amplitude and support length of unbounded solutions are presented for a quasilinear degenerate parabolic nonlinear heat equation with a source. Conclusions reached are based on a method of 'comparison by intersections' with an exact noninvariant solution for the equation with the same period of existence. This comparison also shows the solvability of the Cauchy problem for the equation with a delta function as the initial function.
 Publication:

Zhurnal Vychislitelnoi Matematiki i Matematicheskoi Fiziki
 Pub Date:
 March 1990
 Bibcode:
 1990ZVMMF..30..438G
 Keywords:

 Boundary Value Problems;
 Cauchy Problem;
 Thermal Conductivity;
 Parabolic Differential Equations;
 Roots Of Equations;
 Theorem Proving;
 Fluid Mechanics and Heat Transfer