Two-Sided Estimates of Solutions with a Blow-Up Mode for a Nonlinear Heat Equation with a Quadratic Source

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-07-15 DOI:10.1134/s0001434624050055

Yu. P. Virchenko, V. V. Zhiltsova

引用次数: 0

Abstract

We study compactly supported solutions \(u(x, t) \geq 0\), \(x \in \mathbb{R}\), \(t \geq 0\), of a one-dimensional quasilinear heat transfer equation. The equation has a transport coefficient linear in \(u\) and a self-consistent source \(\alpha u+\beta u^{2}\) of general form. For the blow-up time of compactly supported solutions, we establish two-sided estimates functionally depending on the initial conditions \(u(x, 0)\).

Abstract Image

查看原文本刊更多论文

具有二次源的非线性热方程爆炸模式解的双侧估计值

Abstract 我们研究了一维准线性传热方程的紧凑支撑解 \(u(x, t) \geq 0\), \(x \in \mathbb{R}\), \(t \geq 0\).该方程具有线性于 \(u\) 的传输系数和一般形式的自洽源 \(\alpha u+\beta u^{2}\) 。对于紧凑支撑解的膨胀时间，我们建立了取决于初始条件 \(u(x,0)\)的双面函数估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.