What does this research mean for the field?

Nonnegative solutions of the semilinear heat inequality with Morrey initial data on Riemannian manifolds exhibit bounded estimates under specific initial conditions. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To derive estimates for nonnegative solutions of a semilinear heat inequality involving Morrey initial data over Riemannian manifolds.

February 24, 2026Journal of Evolution Equations0 citationsOpen Access

The semilinear heat inequality with Morrey initial data on Riemannian manifolds

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ADAnuk Dayaprema

Key Points

To derive estimates for nonnegative solutions of a semilinear heat inequality involving Morrey initial data over Riemannian manifolds.
Used a differential inequality framework to analyze nonnegative solutions.
Applied Morrey norms to characterize the initial data on Riemannian manifolds.
Established L-infinity estimates under certain bounds for initial conditions.
Demonstrated that solutions remain bounded under specific Morrey norms.
Provided conditions under which initial data influences long-term behavior of solutions.
Identified ranges for parameters q and s that affect the outcomes of the estimates.

Abstract

Abstract The goal of this paper is to obtain estimates for nonnegative solutions of the differential inequality aligned (t -) u A uᵖ + B u aligned ∂ ∂ t - Δ u ≤ A u p + B u with small initial data in borderline Morrey norms over a Riemannian manifold with bounded geometry. We obtain L^ L ∞ estimates assuming u (, 0) ₌^ₐ, ₂ₐ{₏-₁} + ₀ ₓ ‖ ₔ (·, ₀) ‖ ₌ ₐ, ₂ ₐ ₏ - ₁ + ₒₔ₏ ₀ ≤ ₓ ₓ ‖ ₔ (·, ₓ) ‖ ₋ ₒ ⏓, ₖ₇₄ₑ₄ ₁ ₁ ₐ ≤ ₐ ₂: = ₍ (₏ - ₁) ₂ ₀₍₃ ₁ ₒ ₐ₂ ₁ ≤ ₒ ≤ ₐ ₂. ₀ₒₒₔ₌₈₍₆ ₀₋ₒ₎ ₀ ₁₎ₔ₍₃ ₎₍ ₔ (, ₀) _₌^{ₐ', ' ‖ u (·, 0) ‖ M q ′

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Anuk Dayaprema (2026) studied this question.

synapsesocial.com/papers/699d4028de8e28729cf653d5 https://doi.org/10.1007/s00028-026-01186-x

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February 24, 2026Journal of Evolution Equations0 citationsOpen Access

The semilinear heat inequality with Morrey initial data on Riemannian manifolds

View Full Paper

ADAnuk Dayaprema

Key Points

To derive estimates for nonnegative solutions of a semilinear heat inequality involving Morrey initial data over Riemannian manifolds.
Used a differential inequality framework to analyze nonnegative solutions.
Applied Morrey norms to characterize the initial data on Riemannian manifolds.
Established L-infinity estimates under certain bounds for initial conditions.
Demonstrated that solutions remain bounded under specific Morrey norms.
Provided conditions under which initial data influences long-term behavior of solutions.
Identified ranges for parameters q and s that affect the outcomes of the estimates.

Abstract

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View Full Paper

Cite This Study

Anuk Dayaprema (2026) studied this question.

synapsesocial.com/papers/699d4028de8e28729cf653d5 https://doi.org/10.1007/s00028-026-01186-x

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View Full Paper