Nonlinear Analysis-Real World Applications最新文献

Ocean gyres are modelled by the two-dimensional vorticity equation for inviscid flow on a rotating sphere, since their flow is governed by the tangential velocity components, whereas the vertical velocity component is negligible. From the vorticity equation we derive nonlinear elliptic equations for the square of the meridional velocity component as well as for the azimuthal velocity component. Using maximum principles we then show that, under suitable conditions on the oceanic vorticity, the velocity extrema are attained on the boundary of a subtropical gyre located in the zonal band between 15${}^{\circ }$ and 45${}^{\circ }$ Northern, respectively Southern latitude, where the five major gyres are found.

This paper is concerned with the Dirichlet initial boundary value problem of an epitaxial thin film growth equation involving gradient-type logarithmic nonlinearity and absorption terms. By introducing an equivalent norm and approximating Lipschitz functions, combining with the technique of Faedo–Galerkin approximation and the family of potential wells, we establish the well-posedness of global weak solutions. Meantime, we classify the decay properties and grow-up phenomenon of the considered problem by using the energy functional and the related Nehari manifold.

This paper studies the upper bound of the lifespan of classical solutions of the initial value problems for one dimensional wave equations with quasilinear terms of space-, or time-derivatives of the unknown function. The result for the space-derivative case guarantees the optimality of the general theory for nonlinear wave equations, and its proof is carried out by combination of ordinary differential inequality and iteration method on the lower bound of the weighted functional of the solution.

The main problem addressed in this paper is to study the local existence in time of solutions to the non-homogeneous Neumann initial boundary value problem for the Benjamin–Ono equation on a half-line. In this result, we observe the influence of the boundary data on the behavior of solutions. In order to obtain the characterization of the solution it is essential to use the theory concerning the Riemann–Hilbert problem. We prove local existence in time of the solutions.

In this paper, we formulate a two-strain model with reinfection that combines immunological and epidemiological dynamics across scales, using the COVID-19 pandemic as a case study. Firstly, we conduct a qualitative analysis of both within-host and between-host models. For the within-host model, we prove the existence and stability of equilibria, and Hopf bifurcation occurs from the infection equilibrium with immune response. This implies that, under specific immune states, the virus within an infected individual may persist, and its concentration may also oscillate periodically. For the between-host model, the disease-free equilibrium always exists and is locally asymptotically stable when the epidemiological basic reproduction number ${\Re }^0<1$. In addition, the model can have boundary equilibria of strain 1 or strain 2, which are locally asymptotically stable under specific conditions. However, the co-existence equilibrium does not exist. Secondly, to explore the infection and transmission mechanisms of two strain models and obtain reliable parameter values, we utilize statistical data to fit the immuno-epidemiological model. Simultaneously, we conduct an identifiability analysis of the immuno-epidemiological model to ensure the robustness of the fitted parameters. The results demonstrate the reliable estimation of parameter ranges for structurally unidentifiable parameters with minor measurement errors using the affine invariant ensemble Markov Chain Monte Carlo algorithm (GWMCMC). Moreover, simulations illustrate that enhancing treatment of patients infected with BA.2 strains to inhibit the number of viruses released by infected cells can significantly reduce disease spread.

We consider several classes of degenerate hyperbolic equations involving delay terms and suitable nonlinearities. The idea is to rewrite the problems in an abstract way and, using semigroup theory and energy method, we study well-posedness and stability. Moreover, some illustrative examples are given.

We prove existence of weak solutions to a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot’s equations for poroelasticity, including phase-field dependent material properties, with the Cahn–Hilliard equation to model the evolution of the solid, and is further augmented by a visco-elastic regularization of Kelvin–Voigt type. To obtain this result, we approximate the problem in two steps, where first a semi-Galerkin ansatz is employed to show existence of weak solutions to regularized systems, for which later on compactness arguments allow limit passage. Notably, we also establish a maximal regularity theory for linear visco-elastic problems.

In recent years an increasing interest in more general operators generated by Musielak–Orlicz functions is under development since they provided, in principle, a unified treatment to deal with ordinary and partial differential equations with operators containing the $p$-Laplace operator, the $\varphi$-Laplace operator, operators with variable exponents and the double phase operators. These kind of consideration lead us in García-Huidobro et al. (2024), to consider problems containing the operator ${\left(S(t,u^{\prime })\right)}^{\prime }$, where ${}^{\prime }=\frac{d}{dt}$ and look for period solutions of systems of nonlinear systems of differential equations. In this paper we extend our approach to deal with systems of differential equations containing the operator ${\left(S(t,u^{\prime })\right)}^{\prime }$ this time under Dirichlet, mixed and Neumann boundary conditions. As in García-Huidobro et al. (2024) our approach is to work in $C^1$ spaces to obtain suitable abstract fixed points theorems from which several applications are obtained, including problems of Liénard and Hartman type.

This work is devoted to the analysis of the interplay between internal variables and high-contrast microstructure in inelastic solids. As a concrete case-study, by means of variational techniques, we derive a macroscopic description for an elastoplastic medium. Specifically, we consider a composite obtained by filling the voids of a periodically perforated stiff matrix by soft inclusions. We study the $\Gamma$-convergence of the related energy functionals as the periodicity tends to zero, the main challenge being posed by the lack of coercivity brought about by the degeneracy of the material properties in the soft part. We prove that the $\Gamma$-limit, which we compute with respect to a suitable notion of convergence, is the sum of the contributions resulting from each of the two components separately. Eventually, convergence of the energy minimizing configurations is obtained.

For the Nicholson’s blowflies equation with delayed mortality $N^{\prime }\left(t\right)=m\left(t\right)\left(-\delta N\left(h_1\left(t\right)\right)+PN\left(h_2\left(t\right)\right)e^{-\gamma N\left(h_2\left(t\right)\right)}\right),P>\delta ,$positivity, persistence, and boundedness of solutions are established. Two global stability tests for the positive equilibrium are obtained based on a linearized global stability method, reducing stability of a non-linear model to a specially constructed linear equation. The first one extends the absolute stability result to the case of delayed mortality and the second test is delay-dependent.