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On the existence, regularity and uniqueness of \(L^p\)-solutions to the steady-state 3D Boussinesq system in the whole space and with gravity acceleration
We consider the steady-state Boussinesq system in the whole three-dimensional space, with the action of external forces and the gravitational...
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Multi-phase k-quadrature domains and applications to acoustic waves and magnetic fields
The primary objective of this paper is to explore the multi-phase variant of quadrature domains associated with the Helmholtz equation, commonly...
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Bifurcations and dynamical behaviors for a generalized delayed-diffusive Maginu model
This paper is committed to study the dynamical behaviors of a generalized Maginu model with discrete time delay. We investigate the stability of the...
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Continuity estimates for Riesz potentials on polygonal boundaries
Riesz potentials are well known objects of study in the theory of singular integrals that have been the subject of recent, increased interest from...
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Existence of solutions for superquadratic or asymptotically quadratic fractional Hamiltonian systems
In this paper, we are concerned with a class of periodic fractional Hamiltonian systems when the Hamiltonian is superquadratic not satisfying the...
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Spectral inequality with sensor sets of decaying density for Schrödinger operators with power growth potentials
We prove a spectral inequality (a specific type of uncertainty relation) for Schrödinger operators with confinement potentials, in particular of...
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Energy decay analysis for Porous elastic system with microtemperature: Classical vs second spectrum approach
The stability features of the dissipative porous elastic systems have piqued the interest of several researchers. The desired exponential decay...
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Scattering problems for the wave equation in 1D: D’Alembert-type representations and a reconstruction method
We derive the extension of the classical d’Alembert formula for the wave equation, which provides the analytical solution for the direct scattering...
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Hyper-reduction for parametrized transport dominated problems via adaptive reduced meshes
We propose an efficient residual minimization technique for the nonlinear model-order reduction of parameterized hyperbolic partial differential...
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Global dynamics below a threshold for the nonlinear Schrödinger equations with the Kirchhoff boundary and the repulsive Dirac delta boundary on a star graph
We consider the nonlinear Schrödinger equations on the star graph with the Kirchhoff boundary and the repulsive Dirac delta boundary at the origin....
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Uniform convergence for linear elastostatic systems with periodic high contrast inclusions
We consider the Lamé system of linear elasticity with periodically distributed inclusions whose elastic parameters have high contrast compared to the...
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Hamilton and Li–Yau type gradient estimates for a weighted nonlinear parabolic equation under a super Perelman–Ricci flow
In this paper we derive elliptic and parabolic type gradient estimates for positive smooth solutions to a class of nonlinear parabolic equations on...
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Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions
Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to...
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Solving stationary inverse heat conduction in a thin plate
We consider a steady state heat conduction problem in a thin plate. In the application, it is used to connect two cylindrical containers and fix...
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Stochastic evolution equations with rough boundary noise
We investigate the pathwise well-posedness of stochastic partial differential equations perturbed by multiplicative Neumann boundary noise, such as...
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Sharp well-posedness of the biharmonic Schrödinger equation in a quarter plane
We obtain an almost sharp local well–posedness result for the biharmonic equation on the quarter plane. In addition, we prove that the nonlinear part...
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Combining the hybrid mimetic mixed method with the Scharfetter-Gummel scheme for magnetised transport in plasmas
In this paper, we propose a numerical scheme for fluid models of magnetised plasmas. One important feature of the numerical scheme is that it should...
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Dirac cohomology on manifolds with boundary and spectral lower bounds
Along the lines of the classic Hodge–De Rham theory a general decomposition theorem for sections of a Dirac bundle over a compact Riemannian manifold...
