Pith. Sign in

RECORD

Optimality Conditions for Semilinear Parabolic Equations with Controls in Leading Term

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Hongwei Lou

Optimization and Control · Submitted 19 Aug 2010

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Necessary conditions for optimal controls are established by the method of homogenizing spike variation.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID1008.3360 (version 1)
Pith ID3BCSGHUO, Pith's permanent record of this paper and its review
CitationHongwei Lou. "Optimality Conditions for Semilinear Parabolic Equations with Controls in Leading Term." arXiv:1008.3360 (2010). https://pith.science/paper/3BCSGHUO
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,405 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.07 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.04 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of homogenizing spike variation. Results for problems with state constraints are also stated.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 An optimal control problem for semilinear parabolic partial differential equations is considered. background 0.79 0.51 0.04 asserted 0.92
s1 The control variable appears in the leading term of the equation. background 0.77 0.26 0.04 asserted 1.00
s2 Necessary conditions for optimal controls are established by the method of homogenizing spike variation. method 0.60 0.93 0.66 asserted 1.00
s3 Results for problems with state constraints are also stated. result 0.64 0.83 0.09 asserted 0.98

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of homogenizing spike variation. Results for problems with state constraints are also stated.

Human review

How Pith checks papers → · Full audit of this paper →

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.