This article is cited in 10 papers

Removability of isolated singularities of solutions of quasilinear parabolic equations with absorption

I. I. Skrypnik

Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences

Abstract: This paper is devoted to the investigation of solutions with point singularities for a general quasilinear parabolic equation with absorption. A method for the derivation of new pointwise estimates of a solution and integral estimates of its gradient is developed. Precise conditions on the behaviour of the term characterizing the absorption in the equation that ensure the non-existence of solutions with point singularities are established. The cases of solutions with singularities in the initial plane and in the interior of the domain are considered.

UDC: 517.946

MSC: 35B60, 35K55

Received: 25.11.2004

DOI: 10.4213/sm1397

 English version: Sbornik: Mathematics, 2005, 196:11, 1693–1713

Bibliographic databases:

• 
• 
• 
• 
•