Separability And Compactness, Estimates for the Eigenvalues And Singular Numbers (s-numbers) of a Resolvent of a Class of Singular Parabolic Operators

2023

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DOI 10.21203/rs.3.rs-2862399/v1
Data confidence 70 medium
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Abstract

Abstract In this paper we study a singular parabolic operator$$Lu=\frac{\partial u}{\partial t}-\frac{\partial^2 u}{\partial x^2}+q(x)u$$initially defined on $C^{\infty}_{0,\pi}(\bar{\Omega})$, where $\bar{\Omega}=\{(t,x):-\pi\leq t\leq \pi, -\infty0$ is a constant. {\bf Example.} $q(x)=e^{1000|x|}, -\infty