A discontinuous problem involving the -Laplacian operator and critical exponent in .
A discrete maximum principle [Book]
A discrete phenomenon in propagation of singularities
A distributional solution to a hyperbolic problem arising in population dynamics.
A double -shaped bifurcation curve for a reaction-diffusion model with nonlinear boundary conditions.
A fibering method approach to a system of quasilinear equations with nonlinear boundary conditions
We provide an existence result for a system of quasilinear equations subject to nonlinear boundary conditions on a bounded domain by using the fibering method.
A first order partial differential equation with an integral boundary condition
In questo lavoro si considera un’equazione alle derivate parziali del primo ordine con una condizione sulla frontiera di tipo integrale. Si studia resistenza, l'unicità e il comportamento asintotico delle soluzioni.
A Fractional LC − RC Circuit
Mathematics Subject Classification: 26A33, 30B10, 33B15, 44A10, 47N70, 94C05We suggest a fractional differential equation that combines the simple harmonic oscillations of an LC circuit with the discharging of an RC circuit. A series solution is obtained for the suggested fractional differential equation. When the fractional order α = 0, we get the solution for the RC circuit, and when α = 1, we get the solution for the LC circuit. For arbitrary α we get a general solution which shows how the...
A Fujita-type theorem for the Laplace equation with a dynamical boundary condition.
A functional method applied to operator equations.
A fundamental estimate and an inequality of Caccioppoli's type for nonlinear parabolic systems of higher order
A further improved tanh function method exactly solving the -dimensional dispersive long wave equations.
A Galerkin strategy with Proper Orthogonal Decomposition for parameter-dependent problems – Analysis, assessments and applications to parameter estimation
We address the issue of parameter variations in POD approximations of time-dependent problems, without any specific restriction on the form of parameter dependence. Considering a parabolic model problem, we propose a POD construction strategy allowing us to obtain some a priori error estimates controlled by the POD remainder – in the construction procedure – and some parameter-wise interpolation errors for the model solutions. We provide a thorough numerical assessment of this strategy with the...
A Gamma-convergence argument for the blow-up of a non-local semilinear parabolic equation with Neumann boundary conditions
A general decay estimate for a finite memory thermoelastic Bresse system
This work considers a Bresse system with viscoelastic damping on the vertical displacement and heat conduction effect on the shear angle displacement. A general stability result with minimal condition on the relaxation function is obtained. The system under investigation, to the best of our knowledge, is new and has not been studied before in the literature. What is more interesting is the fact that our result holds without the imposition of the equal speed of wave propagation condition, and differentiation...
A general homogenization result of spectral problem for linearized elasticity in perforated domains
The goal of this paper is to establish a general homogenization result for linearized elasticity of an eigenvalue problem defined over perforated domains, beyond the periodic setting, within the framework of the -convergence theory. Our main homogenization result states that the knowledge of the fourth-order tensor , the -limit of , is sufficient to determine the homogenized eigenvalue problem and preserve the structure of the spectrum. This theorem is proved essentially by using Tartar’s method...
A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction
We establish an asymptotic representation formula for the steady state voltage perturbations caused by low volume fraction internal conductivity inhomogeneities. This formula generalizes and unifies earlier formulas derived for special geometries and distributions of inhomogeneities.
A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction
We establish an asymptotic representation formula for the steady state voltage perturbations caused by low volume fraction internal conductivity inhomogeneities. This formula generalizes and unifies earlier formulas derived for special geometries and distributions of inhomogeneities.
A generalization of Aubry-Mather theory to partial differential equations and pseudo-differential equations
A generalization of the Keller-Segel system to higher dimensions from a structural viewpoint
We consider initial boundary problems of a two-chemical substances chemotaxis system. In the four-dimensional setting, it was shown that solutions exist globally in time and remain bounded if the total mass is less than , whereas the solution emanating from some initial data of large magnitude may blows up. This result can be regarded as a generalization of the well-known problem in the Keller–Segel system to higher dimensions. We will compare mathematical structures of the Keller–Segel system...