We consider a differential operator of order 2n of the type A_n u=(-1)^n (au^(n))^(n), where a(x)>0 in [0,1]∖{x_0} and a(x_0)=0. We show that, for any n∈N, the operator −A_n generates a contractive analytic semigroup of angle π/2 on L^2(0,1). Note that the domain of A_n depends on the type of degeneracy of a. Our theorems extend some previous results in [3] where n=1. .
Fragnelli, G., Goldstein, J.A., Mininni, R., Romanelli, S. (2020). Operators of order 2n with interior degeneracy. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S, 13(12), 3417-3426 [10.3934/dcdss.2020128].
Operators of order 2n with interior degeneracy
Fragnelli, Genni;
2020-01-01
Abstract
We consider a differential operator of order 2n of the type A_n u=(-1)^n (au^(n))^(n), where a(x)>0 in [0,1]∖{x_0} and a(x_0)=0. We show that, for any n∈N, the operator −A_n generates a contractive analytic semigroup of angle π/2 on L^2(0,1). Note that the domain of A_n depends on the type of degeneracy of a. Our theorems extend some previous results in [3] where n=1. .
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https://hdl.handle.net/11365/1274494