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Local Existence of 2D Compressible Current-Vortex Sheets
This survey presents our recent results in Morando et al. 2023, where we establish the local-in-time existence and the nonlinear stability of...
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Ergodic mean field games: existence of local minimizers up to the Sobolev critical case
We investigate the existence of solutions to viscous ergodic Mean Field Games systems in bounded domains with Neumann boundary conditions and local,...
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On a logarithmic wave equation with nonlinear dynamical boundary conditions: local existence and blow-up
This paper deals with a hyperbolic-type equation with a logarithmic source term and dynamic boundary condition. Given convenient initial data, we...
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Local Existence and Uniqueness of Strong Solution to the Inhomogeneous Primitive Equations with Vacuum
In this paper, we establish the existence and uniqueness of the local strong solution to the Cauchy problem of the inhomogeneous incompressible...
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Local and Global Existence and Uniqueness of Solution and Local Well-Posednesss for Abstract Fractional Differential Equations with State-Dependent Delay
We study the local and global existence and uniqueness of solution and the local well-possedness for a general class of abstract fractional...
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Existence of solutions of nonlinear systems subject to arbitrary linear non-local boundary conditions
In this paper, we obtain an explicit expression for the Green’s function of a certain type of systems of differential equations subject to non-local...
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Existence of entropy weak solutions for 1D non-local traffic models with space-discontinuous flux
We study a 1D scalar conservation law whose non-local flux has a single spatial discontinuity. This model is intended to describe traffic flow on a...
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Existence and non-existence of constant scalar curvature and extremal Sasaki metrics
We discuss the existence and non-existence of constant scalar curvature, as well as extremal, Sasaki metrics. We prove that the natural...
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Existence and non-existence results for cooperative elliptic systems without variational structure
We consider general cooperative elliptic systems possibly without variational structure and with differential operator resembling that from an...
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Existence of Local and Maximal Mild Solutions for Some Non-autonomous Functional Differential Equation with Finite Delay
This chapter is devoted to the study of the existence results of local and maximal solutions on the one hand and the existence and uniqueness results...
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Local existence of solutions to 2D Prandtl equations in a weighted Sobolev space
In this work, we investigate two-dimensional nonlinear Prandtl equations on the half plane and prove the local existence of solutions by energy...
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Existence of weak solutions for some local and nonlocal p-Laplacian problem
We study the existence of weak solutions for some elliptic p -Laplacian problems in the case where p depends on the solution itself. We consider two...
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Existence of martingale solutions for stochastic flocking models with local alignment
We establish the existence of martingale solutions to a class of stochastic conservation equations. The underlying models correspond to random...
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Fundamental Definitions and Basic Existence Results
In this chapter we first introduce the basic definitions of global and local solutions of optimization problems on Rn. Then we discuss the...