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Time-periodic weak solutions for a coupled hyperbolic-parabolic system are obtained. A linear heat and wave equation are considered on two respective $d$-dimensional spatial domains that share a common $(d-1)$-dimensional interface…
We study existence, nonexistence, and uniqueness of positive radial solutions for a class of nonlinear systems driven by Pucci extremal operators under a Lane-Emden coupling configuration. Our results are based on the analysis of the…
We consider vacuum solutions of four dimensional general relativity with $\Lambda < 0$. We numerically construct stationary solutions that asymptotically approach a boundary metric with differential rotation. Smooth solutions only exist up…
This paper approaches the question of existence and uniqueness of stationary solutions to a semilinear hyperbolic-parabolic system and the study of the asymptotic behaviour of global solutions. The system is a model for some biological…
Two variable $\Lambda$ models, viz. $\Lambda \sim (\dot a/a)^2$ and $\Lambda \sim \rho$ have been studied under the assumption that the equation of state parameter $\omega$ is a function of time. The selected $\Lambda$ models are found to…
In this Series, we study the weakly nonlinear dynamics of chemically active particles near the threshold for spontaneous motion. In this part, we focus on steady solutions and develop an `adjoint method' for deriving the nonlinear amplitude…
In this article we prove the global existence of a unique strong solution to the initial boundary-value problem for a fourth-order exponential PDE. The equation we study was originally proposed to study the evolution of crystal surfaces,…
We derive an observational constraint on a spherical inhomogeneity of the void centered at our position from the angular power spectrum of the cosmic microwave background(CMB) and local measurements of the Hubble parameter. The late time…
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…
We study some properties of positive solutions to the higher order conformally invariant equation with a singular set $$ (-\Delta)^m u = u^{\frac{n+2m}{n-2m}} ~~~~~~ \textmd{in} ~ \Omega \backslash \Lambda, $$ where $\Omega \subset…
In this paper we show the lower semicontinuity of the global attractors of autonomous thermoelastic plate systems with Neumann boundary conditions when some reaction terms are concentrated in a neighborhood of the boundary and this…
We prove the existence of strong time-periodic solutions and their asymptotic stability with the total energy of the perturbations decaying to zero at an exponential decay rate as $t \rightarrow \infty$ for a semilinear (nonlinearly…
We survey recent work on the properties and decays of mesons as bound states of confined quarks at both zero and finite temperature. The framework for these investigations is the set of QCD Dyson--Schwinger equations truncated to…
We study existence of nonnegative solutions to a nonlinear parabolic boundary value problem with a general singular lower order term and a nonnegative measure as nonhomogeneous datum, of the form $$ \begin{cases} \displaystyle u_t -…
We analyze the spectral properties and peculiar behavior of solutions of a damped wave equation on a finite interval with a singular damping of the form $\alpha/x$, $\alpha>0$. We establish the exponential stability of the semigroup for all…
The singularities of the dynamical response function are one of the most remarkable effects in many-body interacting systems. However in one dimension these divergences only exist strictly at zero temperature, making their observation very…
The paper focuses on the stationary self-consistent problem of magnetic insulation for a vacuum diode with space-charge limitation, described by a singularly perturbed Vlasov-Maxwell system of dimension 1.5. The case of insulated diode when…
In this paper we study the existence of at least two positive weak solutions for an inhomogeneous fourth order equation with Navier boundary data involving nonlinearities of critical growth with a bifurcation parameter $\lambda$ in…
We study a one-dimensional nonlinear hyperbolic-parabolic initial boundary value problem occurring in the theory of thermoelasticity. We prove existence and uniqueness of the local-in-time strong solution. Also, some global-in-time weak…