# Behaviour of solutions of certain quasilinear parabolic equations with power-type non-linearities

## Abstract

The Cauchy problem with non-negative continuous initial function for the equation u{sub t}={delta}u{sup m}-u{sup p}, (x,t) element of S=R{sup N} x R{sub +}, is considered for 0<p<1, p<m. For generalized solutions of this problem with initial data increasing at infinity several results on their behaviour as t{yields}{infinity} are established.

- Authors:

- Pedagogical Institute, Vitebsk (Belarus)

- Publication Date:

- OSTI Identifier:
- 21202918

- Resource Type:
- Journal Article

- Journal Name:
- Sbornik. Mathematics

- Additional Journal Information:
- Journal Volume: 191; Journal Issue: 3; Other Information: DOI: 10.1070/SM2000v191n03ABEH000462; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CAUCHY PROBLEM; EQUATIONS; FUNCTIONS; MATHEMATICAL SOLUTIONS

### Citation Formats

```
Gladkov, A L.
```*Behaviour of solutions of certain quasilinear parabolic equations with power-type non-linearities*. United States: N. p., 2000.
Web. doi:10.1070/SM2000V191N03ABEH000462; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).

```
Gladkov, A L.
```*Behaviour of solutions of certain quasilinear parabolic equations with power-type non-linearities*. United States. doi:10.1070/SM2000V191N03ABEH000462; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).

```
Gladkov, A L. Sun .
"Behaviour of solutions of certain quasilinear parabolic equations with power-type non-linearities". United States. doi:10.1070/SM2000V191N03ABEH000462; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
```

```
@article{osti_21202918,
```

title = {Behaviour of solutions of certain quasilinear parabolic equations with power-type non-linearities},

author = {Gladkov, A L},

abstractNote = {The Cauchy problem with non-negative continuous initial function for the equation u{sub t}={delta}u{sup m}-u{sup p}, (x,t) element of S=R{sup N} x R{sub +}, is considered for 0<p<1, p<m. For generalized solutions of this problem with initial data increasing at infinity several results on their behaviour as t{yields}{infinity} are established.},

doi = {10.1070/SM2000V191N03ABEH000462; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},

journal = {Sbornik. Mathematics},

issn = {1064-5616},

number = 3,

volume = 191,

place = {United States},

year = {2000},

month = {4}

}

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