Singular solutions of fractional elliptic equations with absorption

We prove that there exists a unique very singular solution of the equation, which has self-similar form and we show the convergence of general solutions with suitable initial

By opposition to the power-like case [5], where the initial trace was constructed by duality arguments based upon H¨older inequality and delicate choice of test func- tions, our

Markowich, Complete study of the existence and uniqueness of solutions for semilinear elliptic equations involving measures concentrated on boundary, Complex Var..

and Kuznetsov S.E., Solutions of nonlinear differential equations on a Riemannian manifold and their trace on the Martin boundary, Trans.. & V´eron L., Singular solutions of

A similar variant of this method was used in [1] for the study of extinction properties of solutions of nonstationary diffusion- absorption equations.. Theorem D is obtained

V´eron, Nonlinear second order elliptic equations involving measures, Series in Nonlinear Analysis and Applications 21 , De Gruyter, Berlin/Boston (2013).

4.2 Solutions with a strong singularity. We are particularly interested in the analysis of boundary singularities of such solutions. Furthermore, the scale of the two opposed

7.2 Representation formula for positive solutions. 65 Key words: Nonlinear parabolic equation; Initial trace; Representation formula; Bessel capacities; Borel measure; fine