355 research outputs found

    Traveling wave solutions and spreading speeds for a scalar age-structured equation with nonlocal diffusion

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    In this paper, we study the existence of traveling wave solutions and spreading speeds of a scalar age-structured epidemic model with nonlocal diffusion. Our proofs use the comparison principles to construct suitable sub/super-solutions and to show the regularity of traveling waves solutions

    Existence of multi-dimensional pulsating fronts for KPP equations: a new formulation approach

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    This paper is concerned with the existence of pulsating travelling fronts for a KPP reaction-diffusion equation posed in a multi-dimensional periodic medium. We provide an alternative proof of the classic existence result. Our proof relies largely on the construction of a wave profile under a moving frame, which avoids many technical difficulties in dealing with degenerate elliptic equations. Intriguingly, our analysis also yields that the profile of the front propagating along each rational direction in SN−1\mathbb{S}^{N-1} is periodic in time

    Abstract Parabolic Equations with boundary white noise: an integrated semigroup approach

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    In this paper, we study the existence of solution for stochastic evolution equations with almost sectorial operators and possibly a non dense domain. Such problems cover several types of evolution equations, we are interested here in particular in evolution equations with non-homogenous boundary conditions of white noise type. We obtain the existence and uniqueness of mild solutions in state space using the integrated semigroup theory. The results are applied to stochastic parabolic equations with Neumann boundary conditions
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