Article

A Problem with Nonlocal Boundary Conditions for a Quasilinear Parabolic Equation

T.D. DzhuraevInstitute of Mathematics, Academy of Sciences of Uzbekistan, 29, F. Hodjaev St., Tashkent 700143, UzbekistanJ. O. TakhirovInstitute of Mathematics, Academy of Sciences of Uzbekistan, 29, F. Hodjaev St., Tashkent 700143, Uzbekistan

Georgian Mathematical Journaljournal1999en

ABI

Abstract

Abstract The solvability of the nonlocal boundary value problem 𝑢 𝑡 = 𝑎(𝑡, 𝑥, 𝑢, 𝑢 𝑥 )𝑢 𝑥𝑥 + 𝑏(𝑡, 𝑥, 𝑢, 𝑢 𝑥 ), 0 ≤ 𝑡 ≤ 𝑇, |𝑥| ≤ 𝑙, 𝑢(0, 𝑥) = 0, 𝑢(𝑡, –𝑙) = 𝑢(𝑡, 𝑙), 𝑢 𝑥 (𝑡, –𝑙) = 𝑢 𝑥 (𝑡, 𝑙) in a class of functions is investigated for a quasilinear parabolic equation. The solution uniqueness follows from the maximum principle.

Topics

Differential Equations and Boundary Problems Differential Equations and Numerical Methods Advanced Mathematical Modeling in Engineering

Identifiers

DOI: 10.1515/gmj.1999.421

Citations and references

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