Related papers: Combined effects in nonlinear problems arising in …
In this paper, we develop the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with mixed boundary conditions (Dirichlet and Neumann) for the elasticity equations in high contrast media. By a special…
We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized…
In this article, we study nonlinear Vlasov equations with a smooth interaction kernel on a compact manifold without boundary where the geodesic flow exhibits strong chaotic behavior, known as the Anosov property. We show that, for small…
An initial-and boundary-value problem for the Kelvin-Voigt system, modeling a mixture of n incompressible and viscoelastic fluids, with non-constant density, is investigated in this work. The existence of global-in-time weak solutions is…
Emden-Fowler type equations are nonlinear differential equations that appear in many fields such as mathematical physics, astrophysics and chemistry. In this paper, we perform an asymptotic analysis of a specific Emden-Fowler type equation…
This paper concerns the reconstruction of an anisotropic conductivity tensor in an elliptic second-order equation from knowledge of the so-called power density functionals. This problem finds applications in several coupled-physics medical…
Global existence for the nonisentropic compressible Euler equations with vacuum boundary for all adiabatic constants $\gamma > 1$ is shown through perturbations around a rich class of background nonisentropic affine motions. The notable…
We are concerned with fully nonlinear possibly degenerate elliptic partial differential equations (PDEs) with superlinear terms with respect to $Du$. We prove several comparison principles among viscosity solutions which may be unbounded…
In discrete nonlinear systems, the study of nonlinear waves has revealed intriguing phenomena in various fields such as nonlinear optics, biophysics, and condensed matter physics. Discrete nonlinear Schr\"odinger (DNLS) equations are often…
We consider a reaction-diffusion equation with nonlocal anisotropic diffusion and a linear combination of local and nonlocal monostable-type reactions in a space of bounded functions on $\mathbb{R}^d$. Using the properties of the…
In this work, we study the existence and regularity results of anisotropic elliptic equations with a singular lower order term that grows naturally with respect to the gradient and unbounded coefficients. We take up the following model…
We present several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role. We first focus on…
We establish regularity results for almost-minimizers of a class of variational problems involving both bulk and interface energies. The bulk energy is of Dirichlet type. The surface energy exhibits anisotropic behaviour and is defined by…
We study the existence of solutions for a class of nonlinear Schr\"odinger equations involving a magnetic field with mixed Dirichlet-Neumann boundary conditions. We use Lyusternik-Shnirelman category and the Morse theory to estimate the…
We study nonlinear elliptic equations that arise as stationary states of inhomogeneous nonlinear Schr\"odinger equations with competing singular nonlinearities. The model involves the Laplacian combined with weighted power-type terms and…
We introduce a new quantification of nonuniform ellipticity in variational problems via convex duality, and prove higher differentiability and $2d$-smoothness results for vector valued minimizers of possibly degenerate functionals. Our…
In this paper, we investigate some existence results for double phase anisotropic variational problems involving critical growth. We first establish a Lions type concentration-compactness principle and its variant at infinity for the…
We study the long-time dynamics of the nonlinear processes modeled by diffusion-transport partial differential equations in non-divergence form with drifts. The solutions are subject to some inhomogeneous Dirichlet boundary condition.…
We study Dirichlet problems for fractional Laplace equations of the form $(-\Delta)^{\frac{\alpha}{2}} u = f(x,u)$ in $\mathbb{R}^{n}$ for $0<\alpha<n$ where the nonlinearity $f(x,u) = \sum_{i=1}^{M} \sigma_{i} u^{q_i} + \omega$ involves…
We consider an abstract parabolic problem in a framework of maximal monotone graphs, possibly multi-valued with growth conditions formulated with help of an $x-$dependent $N-$function. The main novelty of the paper consists in the lack of…