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  "title": "When an eroding landscape has a steady shape",
  "shortTitle": "Steady landscapes, coupled drainage",
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  "oneLine": "A constructive local uniqueness theorem links erosion, diffusion and drainage on nonradial domains, with a separate radial theory and channel audit.",
  "abstract": "This analytical candidate studies a landscape whose elevation and downhill drainage must be solved together. Small erosion admits steady states on general smooth domains; constant forcing and a strict flow-growth margin give a locally unique branch with a convergent nested construction and explicit error budgets. Ellipsoids satisfy the geometric margin. A radial theory classifies steady states, relaxation and singular limits. A separate companion supplies wet–dry benchmarks and conditional channel-constraint obstructions. Neither manuscript establishes arbitrary-erosion nonradial existence or general wet–dry evolution.",
  "datePublished": "2026-10-06",
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  "problem": {
    "name": "When can elevation and downhill drainage be solved consistently in the steady stream-power model?",
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  "keywords": [
    "landscape evolution",
    "stream-power erosion",
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    "Small-erosion steady existence with positive variable forcing on smooth bounded domains.",
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    "Continuum residual bounds and a finite inner-stopping rule, conditional on controlled implementation errors.",
    "All-positive-parameter radial steady theory and radial relaxation for n≥1.",
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  "relatedWorks": [
    {
      "citation": "Richter (1981). An inverse problem for the steady state diffusion equation. Classical prescribed-potential reconstruction; full text inspected during revision.",
      "url": "https://doi.org/10.1137/0141016",
      "doi": "10.1137/0141016"
    },
    {
      "citation": "Anand et al. (2023). Self-similarity and vanishing diffusion in fluvial landscapes. Earlier one-dimensional profiles and small-diffusion analysis.",
      "url": "https://doi.org/10.1073/pnas.2302401120",
      "doi": "10.1073/pnas.2302401120"
    },
    {
      "citation": "Binard, Degond and Noble (2024). Well-posedness and stability analysis of a landscape evolution model. A distinct three-field positive-depth system.",
      "url": "https://doi.org/10.1007/s00332-023-09997-9",
      "doi": "10.1007/s00332-023-09997-9"
    },
    {
      "citation": "Díaz et al. (2008). Mathematical analysis of a model of river channel formation. Source of the formulation examined in the companion.",
      "url": "https://doi.org/10.1007/s00024-004-0394-3",
      "doi": "10.1007/s00024-004-0394-3"
    },
    {
      "citation": "Litwin et al. (2025). Hillslope diffusion and channel steepness in landscape evolution models. Scaling and physical-model distinctions.",
      "url": "https://doi.org/10.5194/esurf-13-277-2025",
      "doi": "10.5194/esurf-13-277-2025"
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