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  "body": "\n## Summary\n\nA quasilinear PDE is a [[partial differential equation|GC5BDZ6QBC]] that is linear in the highest-order derivatives of the unknown.\nIts coefficients may depend on the unknown and its lower-order derivatives.\nThis class contains the equations of fluid dynamics, the [[minimal surface equation|3GV2E2YTZX]] and the [[p-Laplace equation|XJMYGY0ZZF]].\nIt sits between [[semilinear|RCNY89A4NY]] and [[fully nonlinear|2D3N1ZJWBW]] equations.\nSee the [[definition|DV92N2YWZJ]].\n\n## Explanations\n\n### L1 human\n\nIn a quasilinear equation the highest derivatives still enter one at a time, multiplied by coefficients.\nBut these coefficients may depend on the solution itself.\nIn [[Burgers' equation|NEGHXN8RE1]] $\\partial_t u + u \\, \\partial_x u = 0$, the speed at which a wave moves is the value $u$ of the wave.\nSo high parts of the wave overtake low parts, and the solution can form a shock in finite time.\n",
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  "name": "Quasilinear PDE",
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