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About: Nonlinear partial differential equation

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In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear terms. They describe many different physical systems, ranging from gravitation to fluid dynamics, and have been used in mathematics to solve problems such as the Poincaré conjecture and the Calabi conjecture. They are difficult to study: almost no general techniques exist that work for all such equations, and usually each individual equation has to be studied as a separate problem.

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  • In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear terms. They describe many different physical systems, ranging from gravitation to fluid dynamics, and have been used in mathematics to solve problems such as the Poincaré conjecture and the Calabi conjecture. They are difficult to study: almost no general techniques exist that work for all such equations, and usually each individual equation has to be studied as a separate problem. The distinction between a linear and a nonlinear partial differential equation is usually made in terms of the properties of the operator that defines the PDE itself. (en)
  • 非线性偏微分方程起源於各種應用科學中，如固體力學，流體力學，聲學，非線性光學，等離子體物理學，量子場論等學科。 函數關係 F=0 是一個廣義的偏微分方程，如果 u，v 是此微分方程的兩個解，而（au+bv) 也是此微分方程的解，則此偏微分方程稱為線性偏微分方程，否則稱為非線性偏微分方程。 (zh)
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  • 1117518387 (xsd:integer)
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  • 2018-12-12 (xsd:date)
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  • S.I. (en)
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  • N/n067170 (en)
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  • Pokhozhaev (en)
dbp:title
  • Non-linear partial differential equation (en)
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  • 非线性偏微分方程起源於各種應用科學中，如固體力學，流體力學，聲學，非線性光學，等離子體物理學，量子場論等學科。 函數關係 F=0 是一個廣義的偏微分方程，如果 u，v 是此微分方程的兩個解，而（au+bv) 也是此微分方程的解，則此偏微分方程稱為線性偏微分方程，否則稱為非線性偏微分方程。 (zh)
  • In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear terms. They describe many different physical systems, ranging from gravitation to fluid dynamics, and have been used in mathematics to solve problems such as the Poincaré conjecture and the Calabi conjecture. They are difficult to study: almost no general techniques exist that work for all such equations, and usually each individual equation has to be studied as a separate problem. (en)
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  • Nonlinear partial differential equation (en)
  • 非线性偏微分方程 (zh)
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