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Title: On the Log-Laplace Equation for Nonlocal Operators Generating Sub-Markovian Semigroups

Abstract

We consider the semilinear Cauchy problem for a class of pseudo-differential operators generating sub-Markovian semigroups. Solutions of such problems with negative definite nonlinearity play an important role in constructing branching measure-valued processes. We establish local existence and uniqueness of solutions in the context of the Dirichlet space associated to the problem. Comparison and global properties of solutions are also studied.

Authors:
 [1];  [2]
  1. Department of Mathematics, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, Wales (United Kingdom), E-mail: N.Jacob@swansea.ac.uk
  2. Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW (United Kingdom), E-mail: V.Moroz@bristol.ac.uk
Publication Date:
OSTI Identifier:
21067492
Resource Type:
Journal Article
Journal Name:
Applied Mathematics and Optimization
Additional Journal Information:
Journal Volume: 45; Journal Issue: 2; Other Information: DOI: 10.1007/s00245-001-0037-3; Copyright (c) Inc. 2001 Springer-Verlag New York; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0095-4616
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CAUCHY PROBLEM; DIRICHLET PROBLEM; GROUP THEORY; LAPLACE EQUATION; MARKOV PROCESS; MATHEMATICAL OPERATORS; MATHEMATICAL SOLUTIONS; MATHEMATICAL SPACE; MEASURE THEORY; NONLINEAR PROBLEMS

Citation Formats

Jacob, N., and Moroz, V. On the Log-Laplace Equation for Nonlocal Operators Generating Sub-Markovian Semigroups. United States: N. p., 2002. Web. doi:10.1007/S00245-001-0037-3.
Jacob, N., & Moroz, V. On the Log-Laplace Equation for Nonlocal Operators Generating Sub-Markovian Semigroups. United States. doi:10.1007/S00245-001-0037-3.
Jacob, N., and Moroz, V. Mon . "On the Log-Laplace Equation for Nonlocal Operators Generating Sub-Markovian Semigroups". United States. doi:10.1007/S00245-001-0037-3.
@article{osti_21067492,
title = {On the Log-Laplace Equation for Nonlocal Operators Generating Sub-Markovian Semigroups},
author = {Jacob, N. and Moroz, V.},
abstractNote = {We consider the semilinear Cauchy problem for a class of pseudo-differential operators generating sub-Markovian semigroups. Solutions of such problems with negative definite nonlinearity play an important role in constructing branching measure-valued processes. We establish local existence and uniqueness of solutions in the context of the Dirichlet space associated to the problem. Comparison and global properties of solutions are also studied.},
doi = {10.1007/S00245-001-0037-3},
journal = {Applied Mathematics and Optimization},
issn = {0095-4616},
number = 2,
volume = 45,
place = {United States},
year = {2002},
month = {7}
}