Solution of nonlinear partial differential equations by the geometric method

被引：0

作者：

Rubina, L. I. ^{[1
]}

Ulyanov, O. N. ^{[2
]}

机构：

[1] Russian Acad Sci, Inst Math & Mech, Ural Branch, Moscow, Russia

[2] Ural Federal Univ, Russian Acad Sci, Inst Math & Mech, Ural Branch, Ekaterinburg, Russia

来源：

TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN | 2012年 / 18卷 / 02期

关键词：

nonlinear partial differential equations; heat equation; equation for the flow function in a boundary layer; exact solutions;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The earlier proposed geometric method of investigation of nonlinear partial differential equations is developed. The heat equation describing blow-up regimes and the equation for the flow function in a boundary layer are studied. We propose a modification of the method based on the specific character of the equations and show its applicability in the case under consideration. Classes of particular exact solutions are found and a boundary value problem is solved.

引用

页码：265 / 280

页数：16

共 11 条

[1]

GRADSHTEYN IS, 1962, TABLITSY INTEGRALOV

[2]

Kamke E., 1966, SPRAVOCHNIK DIFFEREN

[3]

KURANT P, 1964, URAVNENIYA S CHASTNY

[4]

KURKINA ES, 2008, DIFF URAVN, P512

[5]

LOITSYANSKIY LG, 1957, MEKHANIKA ZHIDKOSTI

[6]

LOMKATSI TD, 1967, TABLITSY ELLIPTICHES

[7] CONICAL REFRACTION IN CRYSTAL OPTICS AND HYDROMAGNETICS [J].

LUDWIG, D .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1961, 14 (02) :113-&

[8]

Rubina LI, 2008, T I MAT MEKH URO RAN, V14, P130

[9]

Rubina LI, 2010, T I MAT MEKH URO RAN, V16, P209

[10]

RUBINA LI, 1972, PRIKL MAT MEKH, V36, P435

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