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Title: Existence in the Sense of Sequences of Stationary Solutions for Some Non-Fredholm Integro-Differential Equations

Abstract

We establish the existence in the sense of sequences of stationary solutions for some reaction-diffusion type equations in appropriate H{sup 2} spaces. It is shown that, under reasonable technical conditions, the convergence in L{sup 1} of the integral kernels implies the existence and convergence in H{sup 2} of solutions. The nonlocal elliptic equations involve second order differential operators with and without the Fredholm property. Bibliography: 21 titles.

Authors:
 [1];  [2]
  1. University of Toronto (Canada)
  2. University Lyon 1, Institute Camille Jordan, UMR 5208 CNRS (France)
Publication Date:
OSTI Identifier:
22771585
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Sciences
Additional Journal Information:
Journal Volume: 228; Journal Issue: 6; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CONVERGENCE; DIFFERENTIAL OPERATORS; DIFFUSION EQUATIONS; INTEGRALS; INTEGRO-DIFFERENTIAL EQUATIONS; KERNELS; MATHEMATICAL SOLUTIONS; MATHEMATICAL SPACE

Citation Formats

Vougalter, V., E-mail: vitali@math.toronto.edu, and Volpert, V., E-mail: volpert@math.univ-lyon1.fr. Existence in the Sense of Sequences of Stationary Solutions for Some Non-Fredholm Integro-Differential Equations. United States: N. p., 2018. Web. doi:10.1007/S10958-017-3650-7.
Vougalter, V., E-mail: vitali@math.toronto.edu, & Volpert, V., E-mail: volpert@math.univ-lyon1.fr. Existence in the Sense of Sequences of Stationary Solutions for Some Non-Fredholm Integro-Differential Equations. United States. doi:10.1007/S10958-017-3650-7.
Vougalter, V., E-mail: vitali@math.toronto.edu, and Volpert, V., E-mail: volpert@math.univ-lyon1.fr. Thu . "Existence in the Sense of Sequences of Stationary Solutions for Some Non-Fredholm Integro-Differential Equations". United States. doi:10.1007/S10958-017-3650-7.
@article{osti_22771585,
title = {Existence in the Sense of Sequences of Stationary Solutions for Some Non-Fredholm Integro-Differential Equations},
author = {Vougalter, V., E-mail: vitali@math.toronto.edu and Volpert, V., E-mail: volpert@math.univ-lyon1.fr},
abstractNote = {We establish the existence in the sense of sequences of stationary solutions for some reaction-diffusion type equations in appropriate H{sup 2} spaces. It is shown that, under reasonable technical conditions, the convergence in L{sup 1} of the integral kernels implies the existence and convergence in H{sup 2} of solutions. The nonlocal elliptic equations involve second order differential operators with and without the Fredholm property. Bibliography: 21 titles.},
doi = {10.1007/S10958-017-3650-7},
journal = {Journal of Mathematical Sciences},
issn = {1072-3374},
number = 6,
volume = 228,
place = {United States},
year = {2018},
month = {2}
}