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Maitere Aguerrea

Publications and source records attributed to Maitere Aguerrea.

6 recordsLinked to original sources
arXiv2015

On existence of semi-wavefronts for a non-local reaction-diffusion equations with distributed time delay

We establish the existence of semi-wavefronts solutions for a non-local delayed reaction-diffusion equation with monostable nonlinearity. The existence result is proved for all speeds $c\geq c_\star$, where the determination of $c_\star$ is similar to the calculation of the minimal speed of propagation. The results are applied to some non-local reaction-diffusion epidemic and population models with distributed time delay.

math.AP↗
arXiv2015

Existence and Properties of Semi-Bounded Global Solutions to the Functional Differential Equation with Volterra's Type Operators on the Real Line

Consider the equation $$ u'(t)=\ell_0(u)(t)-\ell_1(u)(t)+f(u)(t)\qquad\mbox{for~a.~e.~}\,t\in\mathbb{R} $$ where $\ell_i:C_{loc}\big(\mathbb{R};\mathbb{R}\big)\to L_{loc}\big(\mathbb{R};\mathbb{R}\big)$ $(i=0,1)$ are linear positive continuous operators and $f:C_{loc}\big(\mathbb{R};\mathbb{R}\big)\to L_{loc}\big(\mathbb{R};\mathbb{R}\big)$ is a continuous operator satisfying the local Carathéodory conditions. The efficient conditions guaranteeing the existence of a global solution, which is bounded and non-negative in the neighbourhood of $-\infty$, to the equation considered are established provided $\ell_0$, $\ell_1$, and $f$ are Volterra's type operators. The existence of a solution which is positive on the whole real line is discussed, as well. Furthermore, the asymptotic properties of such solutions are studied in the neighbourhood of $-\infty$. The results are applied to certain models appearing in natural sciences.

math.AP↗
arXiv2013

On the uniqueness of semi-wavefronts for non-local delayed reaction-diffusion equations

We establish the uniqueness of semi-wavefront solution for a non-local delayed reaction-diffusion equation. This result is obtained by using a generalization of the Diekman-Kaper theory for a nonlinear convolution equation. Several applications to the systems of non-local reaction-diffusion equations with distributed time delay are also considered.

math.AP↗
arXiv2010

On uniqueness of semi-wavefronts (Diekmann-Kaper theory of a nonlinear convolution equation re-visited)

Motivated by the uniqueness problem for monostable semi-wavefronts, we propose a revised version of the Diekmann and Kaper theory of a nonlinear convolution equation. Our version of the Diekmann-Kaper theory allows 1) to consider new types of models which include nonlocal KPP type equations (with either symmetric or anisotropic dispersal), non-local lattice equations and delayed reaction-diffusion equations; 2) to incorporate the critical case (which corresponds to the slowest wavefronts) into the consideration; 3) to weaken or to remove various restrictions on kernels and nonlinearities. The results are compared with those of Schumacher (J. Reine Angew. Math. 316: 54-70, 1980), Carr and Chmaj (Proc. Amer. Math. Soc. 132: 2433-2439, 2004), and other more recent studies.

math.CA↗
arXiv2008

Uniqueness of fast travelling fronts in reaction-diffusion equations with delay

We consider positive travelling fronts of the time-delayed reaction-diffusion equation with the monostable birth function. Our main result says that for every fixed and sufficiently large velocity c, the positive travelling front is unique (modulo translations). To prove the uniqueness, we introduce a small parameter 1/c and realize the Lyapunov-Schmidt reduction in a scale of Banach spaces.

math.AP↗