A new family of boundary-domain integral equations for the diffusion equation with variable coefficient in unbounded domains

Carlos Fresneda-Portillo

doi:10.3934/cpaa.2020228

Article Contents

2020, Volume 19, Issue 11: 5097-5114. Doi: 10.3934/cpaa.2020228

This issue Previous Article Existence and concentration of nodal solutions for a subcritical p&q equation Next Article Normalized solutions for 3-coupled nonlinear Schrödinger equations

A new family of boundary-domain integral equations for the diffusion equation with variable coefficient in unbounded domains

Carlos Fresneda-Portillo

School of Engineering, Computing and Mathematics, Wheatley Campus, Oxford Brookes University, OX33 1HX, Wheatley, UK

Received: February 29, 2020

Revised: April 30, 2020

Early access: July 2020

Published: November 2020

This research was supported by the grants 1636273 from the EPSRC

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Abstract

A system of Boundary-Domain Integral Equations is derived from the mixed (Dirichlet-Neumann) boundary value problem for the diffusion equation in inhomogeneous media defined on an unbounded domain. This paper extends the work introduced in [25] to unbounded domains. Mapping properties of parametrix-based potentials on weighted Sobolev spaces are analysed. Equivalence between the original boundary value problem and the system of BDIEs is shown. Uniqueness of solution of the BDIEs is proved using Fredholm Alternative and compactness arguments adapted to weigthed Sobolev spaces.

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Mathematics Subject Classification: Primary: 35J57, 45F15; Secondary: 45P05.

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