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Employing the Einstein-scalar field system, we demonstrate an approach for proving high co-dimensional nonlinear instability of naked-singularity solutions as constructed by Christodoulou in [18]. We further investigate the censorship of…
In this article we derive rigorously a nonlinear, steady, bifurcation through spectral bifurcation (i.e., eigenvalues of the linearized equation crossing the imaginary axis) for a class of hyperbolic-parabolic model in a strip. This is…
In the present work, we introduce a discrete formulation of the nonlinear Dirac equation in the form of a discretization of the Gross-Neveu model. The motivation for this discrete model proposal is both computational (near the continuum…
The main purpose of the present paper is to investigate the nonlinear stability of viscous shock waves and rarefaction wave for bipolar Vlasov-Poisson-Boltzmann (VPB) system. To this end, motivated by the micro-macro decomposition to the…
Internal waves describe the (linear) response of an incompressible stably stratified fluid to small perturbations. The inclination of their group velocity with respect to the vertical is completely determined by their frequency. Therefore…
We study the weak solvability of a nonlinearly coupled system of parabolic and pseudo-parabolic equations describing the interplay between mechanics, chemical reactions, diffusion and flow in a mixture theory framework. Our approach relies…
We transform the two-matrix model, studied by P.Di Francesco and al., into a normal one-matrix model by identifying a ``formal'' integral used by these authors as a proper integral. We show also, using their method, that the results…
We derive the exact analytical solutions to the symmetron field theory equations in the presence of a one or two mirror system in the case of a spontaneously broken phase in vacuum as well as in matter. This complements a similar analysis…
We consider a non-polynomial cubic spline to develop the classes of methods for the numerical solution of singularly perturbed two-point boundary value problems. The proposed methods are second and fourth order accurate and applicable to…
This paper is concerned with the theory of generic non-normal nonlinear evolutionary equations, with potential applications in Fluid Dynamics and Optics. Two theoretical models are presented. The first is a model two-level non-normal…
In this paper we deal with a doubly nonlinear Cahn-Hilliard system, where both an internal constraint on the time derivative of the concentration and a potential for the concentration are introduced. The definition of the chemical potential…
This paper proves existence and stability results of solitary-wave solutions to coupled nonlinear Schr\"{o}dinger equations with power-type nonlinearities arising in several models of modern physics. The existence of solitary waves is…
We study existence and uniqueness of solutions to a class of nonlinear degenerate parabolic equations, in bounded domains. We show that there exists a unique solution which satisfies possibly inhomogeneous Dirichlet boundary conditions. To…
We apply the singular sequence method to investigate the finiteness problem for stationary configurations of the planar N-vortex problem. The initial step of the singular sequence method involves identifying all two-colored diagrams. These…
We provide a complete description of perturbative unitarity bounds on the gauge-scalar sectors of models with extra $SU(2)$ doublet, neutral singlet, and charged singlet scalars. Such additions are very frequent in models beyond the…
We deal with the problem of description of nonsingular pairs of compatible flat metrics for the general $N$-component case. We describe the scheme of the integrating the nonlinear equations describing nonsingular pairs of compatible flat…
In this paper we introduce a new fix point iteration scheme for solving nonlinear electromagnetic scattering problems. The method is based on a spectral formulation of Maxwell's equations called the Bidirectional Pulse Propagation…
We study a regularization of the classical Saint-Venant (shallow-water) equations, recently introduced by D. Clamond and D. Dutykh (Commun. Nonl. Sci. Numer. Simulat. 55 (2018) 237-247). This regularization is non-dispersive and formally…
It is studied the Cauchy problem for the equations of Burgers' type but with bounded dissipation flux. Such equations degenerate to hyperbolic ones as the velocity gradient tends to infinity. Thus the discontinuous solutions are permitted.…
This note studies a four-field hyperbolic PDE model that was recently introduced by Bemfica, Disconzi, and Noronha for the pure radiation fluid with viscosity, and asks whether shock waves admit continuous profiles in this description. The…