On the solvability conditions for the diffusion      equation with convection terms

Vitali Vougalter; Vitaly Volpert

doi:10.3934/cpaa.2012.11.365

Article Contents

2012, Volume 11, Issue 1: 365-373. Doi: 10.3934/cpaa.2012.11.365

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On the solvability conditions for the diffusion equation with convection terms

Vitali Vougalter^1, and
Vitaly Volpert^2,

1.
University of Cape Town, Department of Mathematics, Rondebosch, 7701
2.
Institute of Mathematics, University Lyon 1, 69622 Villeurbann

Received: January 2010

Revised: August 2010

Published: January 2012

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Abstract

A linear second order elliptic equation describing heat or mass diffusion and convection on a given velocity field is considered in $R^3$. The corresponding operator $L$ may not satisfy the Fredholm property. In this case, solvability conditions for the equation $L u = f$ are not known. In this work, we derive solvability conditions in $H^2(R^3)$ for the non self-adjoint problem by relating it to a self-adjoint Schrödinger type operator, for which solvability conditions are obtained in our previous work [13].

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Mathematics Subject Classification: Primary: 35J10, 35P10; Secondary: 35P25.

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