Search results for "global solution"
showing 4 items of 4 documents
Stationary, Oscillatory, Spatio-Temporal Patterns and Existence of Global Solutions in Reaction-Diffusion Models of Three Species
2023
The goal of my Ph.D. research is to analyze three species models in order to describe the behavior of an ecological community. In particular, two reaction-diffusion systems describing different local interactions between three species have been considered to obtain species coexistence, diversity, and distribution patterns. The first analyzed model describes intraguild predation: there are an IG-predator species, an IG-prey species, and a common resource species, which is shared by both of them. The IGP interaction is of Lotka-Volterra type, coupled with nonlinear diffusion, since we assume that the IG-prey moves towards lower density areas of the IG-predator. In this model, the extinction o…
A general nonexistence result for inhomogeneous semilinear wave equations with double damping and potential terms
2021
Abstract We investigate the large-time behavior of solutions for a class of inhomogeneous semilinear wave equations involving double damping and potential terms. Namely, we first establish a general criterium for the absence of global weak solutions. Next, some special cases of potential and inhomogeneous terms are studied. In particular, when the inhomogeneous term depends only on the variable space, the Fujita critical exponent and the second critical exponent in the sense of Lee and Ni are derived.
On a Fractional in Time Nonlinear Schrödinger Equation with Dispersion Parameter and Absorption Coefficient
2020
This paper is concerned with the nonexistence of global solutions to fractional in time nonlinear Schrö
Nonexistence Results for Higher Order Fractional Differential Inequalities with Nonlinearities Involving Caputo Fractional Derivative
2021
Higher order fractional differential equations are important tools to deal with precise models of materials with hereditary and memory effects. Moreover, fractional differential inequalities are useful to establish the properties of solutions of different problems in biomathematics and flow phenomena. In the present work, we are concerned with the nonexistence of global solutions to a higher order fractional differential inequality with a nonlinearity involving Caputo fractional derivative. Namely, using nonlinear capacity estimates, we obtain sufficient conditions for which we have no global solutions. The a priori estimates of the structure of solutions are obtained by a precise analysis …