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arXiv · 2207.03731

Solvability of a semilinear heat equation on Riemannian manifolds

Jin Takahashi·Hikaru Yamamoto
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Abstract

We study the solvability of the initial value problem for the semilinear heat equation $u_t-\Delta u=u^p$ in a Riemannian manifold $M$ with a nonnegative Radon measure $\mu$ on $M$ as initial data. We give sharp conditions on the local-in-time solvability of the problem for complete and connected $M$ with positive injectivity radius and bounded sectional curvature.

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Jin Takahashi, Hikaru Yamamoto. 2022-07-08. Solvability of a semilinear heat equation on Riemannian manifolds. https://arxiv.org/abs/2207.03731

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