Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Existence of solutions semilinear parabolic equations with singular initial data in the Heisenberg group (2408.16985v1)

Published 30 Aug 2024 in math.AP

Abstract: In this paper we obtain necessary conditions and sufficient conditions on the initial data for the solvability of fractional semilinear heat equations with power nonlinearities in the Heisenberg group $\mathbb{H}N$. Using these conditions, we can prove that $1+2/Q$ separates the ranges of exponents of nonlinearities for the global-in-time solvability of the Cauchy problem (so-called the Fujita-exponent), where $Q=2N+2$ is the homogeneous dimension of $\mathbb{H}N$, and identify the optimal strength of the singularity of the initial data for the local-in-time solvability. Furthermore, our conditions lead sharp estimates of the life span of solutions with nonnegative initial data having a polynomial decay at the space infinity.

Citations (1)

Summary

We haven't generated a summary for this paper yet.