Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 321-328

ON THE EXISTENCE OF STATIONARY SOLUTIONS FOR SOME NONLINEAR HEAT EQUATIONS

Vitaly Volpert and Vitali Vougalter

University Lyon 1, Institute Camille Jordan, UMR 5208 CNRS
Villeurbanne, 69622, France; volpert 'at' math.univ-lyon1.fr

University of Toronto, Department of Mathematics
Toronto, Ontario, M5S 2E4, Canada; vitali 'at' math.toronto.edu

Abstract. We establish the existence in H³(R⁵) of stationary solutions of certain nonlinear heat equations using the Fixed Point Technique. The equation for the perturbed solution involves the second order differential operator without Fredholm property.

2010 Mathematics Subject Classification: Primary 35J05, 35P30, 47F05.

Key words: Nonlinear heat equations, non Fredholm operators, Sobolev spaces.

Reference to this article: V. Volpert and V. Vougalter: On the existence of stationary solutions for some nonlinear heat equations. Ann. Acad. Sci. Fenn. Math. 40 (2015), 321-328.

Full document as PDF file

doi:10.5186/aasfm.2015.4013