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Roger Tagne Wafo

Publications and source records attributed to Roger Tagne Wafo.

7 recordsLinked to original sources
arXiv2025

Global stability analysis of an age-structured model assessing the impact of Radopholus similis on banana-plantain production

In this paper, we develop and analyse a mathematical model to investigate the interactions between banana and plantain plants and the nematode \textit{Radopholus similis}, a pest species occurring in banana plantations worldwide, with particularly high prevalence in Central Africa. The model incorporates root infection and mortality rates as functions of root age, providing a more realistic representation of the infection dynamics. We prove that the model is well-defined by establishing the existence and uniqueness of a mild solution using the theory of semi-groups for nonlinear evolutionary systems. We further show that the solution is positive and bounded. Under additional assumptions on the regularity of the parameters and the data, we prove that the mild solution is indeed a classical solution. We then study the asymptotic behaviour of the solution by deriving a threshold parameter \(\mathcal{N}\), which determines the stability of the disease-free equilibrium. Finally, we perform a numerical analysis of the proposed model using the semi-implicit Euler method. The biological consistency of the numerical solutions is established, and simulations are carried out to illustrate the theoretical results and estimate yield losses caused by nematodes. We conclude the numerical analysis by implementing an impulsive control strategy, which confirms that the use of nematicides - whether chemical or biological - helps to mitigate the devastating effects of nematodes and enhances crop yield.

math.AP↗
arXiv2019

Global Dynamics for a relativistic charged and colliding plasma in presence of a massive scalar field on the Robertson-Walker spacetime

We consider the coupled Einstein-Maxwell-Boltzmann system with cosmological constant in presence of a massive scalar field. The background metric is that of Friedman-Lemaître-Robertson-Walker space time in the spatially homogeneous case where the unknown functions only depend on time and not on the space variables $(x^i)$, $i=1,2,3$. By combining the energy estimates method with that of characteristics we derive under suitable conditions on the chock kernel (see Eq. 2.20), a local (in time) solution of the coupled system. Further, under the hypotheses that the data are small in some appropriate norms and that the cosmological constant satisfies $Λ> -4πm^2Φ_0^2$, we derive a unique global (in time) solution (Theorem 6.1).

math.AP↗
arXiv2016

On the characteristic initial value problem for nonlinear symmetric hyperbolic systems, including Einstein equations

We consider a characteristic initial value problem for a class of symmetric hyperbolic systems with initial data given on two smooth null intersecting characteristic surfaces. We prove existence of solutions on a future neighborhood of the initial surfaces. The general result is applied to general semilinear wave equations, as well as the Einstein equations with or without sources, and conformal variations thereof.

gr-qc↗
arXiv2014

Initial value problems for wave equations on manifolds

We study the global theory of linear wave equations for sections of vector bundles over globally hyperbolic Lorentz manifolds. We introduce spaces of finite energy sections and show well-posedness of the Cauchy problem in those spaces. These spaces depend in general on the choice of a time function but it turns out that certain spaces of finite energy solutions are independent of this choice and hence invariantly defined. We also show existence and uniqueness of solutions for the Goursat problem where one prescribes initial data on a characteristic partial Cauchy hypersurface. This extends classical results due to Hörmander.

math.AP↗
arXiv2013

Solutions with a uniform time of existence of a class of characteristic semi-linear wave equations near S+

We prove existence and uniqueness of solution of a class of semi-linear wave equations with initial data prescribed on the light-cone with vertex the origin of a Minkowski space-time. The nonlinear term is assumed to satisfy a nullity condition which guarantee that the neighborhood of the initial cone on which we obtain our solution does not shrink to zero as one approaches infinity. This result is applied to wave maps on Minkowski space-time $\R^{n+1}$ with $n\ge 3$.

math.AP↗
arXiv2010

Solutions of quasi-linear wave equations polyhomogeneous at null infinity in high dimensions

We prove propagation of weighted Sobolev regularity for solutions of the hyperboloidal Cauchy problem for a class of quasi-linear symmetric hyperbolic systems, under structure conditions compatible with the Einstein-Maxwell equations in space-time dimensions $n+1\ge 7$. Similarly we prove propagation of polyhomogeneity in dimensions $n+1\ge 9$. As a byproduct we obtain, in those last dimensions, polyhomogeneity at null infinity of small data solutions of vacuum Einstein, or Einstein-Maxwell equations evolving out of initial data which are stationary outside of a ball.

gr-qc↗