Exact estimates of the amplitude and support of unbounded solutions of the nonlinear heat equation with a source
Abstract
Exact upper-bound estimates of the amplitude and support length of unbounded solutions are presented for a quasi-linear 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