ScholarLens Back to search
1995•Sbornik MathematicsOpen access

The Cauchy problem in classes of increasing functions for the equation of filtration with convection

Alexander L'vovich Gladkov

Open full text 7 citations

Abstract

We consider the Cauchy problem with a non-negative continuous initial function for the equation ut=(um)xx+c(un)x where m > l, m≥n, n≥1 and c is a positive constant. We prove a number of existence and uniqueness theorems for generalized solutions increasing at infinity for this Cauchy problem; we also investigate the behaviour of these solutions for large values of the time.

Open-access reader

About this research paper

What this paper is about

We consider the Cauchy problem with a non-negative continuous initial function for the equation ut=(um)xx+c(un)x where m > l, m≥n, n≥1 and c is a positive constant. We prove a number of existence and uniqueness theorems for generalized solutions increasing at infinity for this Cauchy problem; we also investigate the behaviour of these solutions for large values of the time.

Why it matters

OpenAlex reports 7 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

We consider the Cauchy problem with a non-negative continuous initial function for the equation ut=(um)xx+c(un)x where m > l, m≥n, n≥1 and c is a positive constant. We prove a number of existence and uniqueness theorems for generalized solutions increasing at infinity for this Cauchy problem; we also investigate the behaviour of these solutions for large values of the time.

Key concepts: Uniqueness, Mathematics, Initial value problem, Cauchy problem, Filtration (mathematics), Constant (computer programming), Infinity, Cauchy distribution

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
The Cauchy problem in classes of increasing functions for the equation of filtration with convection — Research Paper | ScholarLens