| Contents |
| The main goal of this talk is to prove that every non-negative
strong solution $u(x,t)$ to the nonlocal heat equation, can be written as
$$u(x,t)=\int_{\mathbb{R}^{n}}{p(x-y,t)u(y,0)\, dy},$$
where $p(x,t)$ is the fundamental solution. This result shows uniqueness in the setting of non-negative
solutions and extends some classical results for the heat equation by D. V. Widder to the
nonlocal diffusion framework. Work done in collaboration with I. Peral , F. Soria and E. Valdinoci. |
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