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Energy conservation for the weak solutions to the 3D compressible nematic liquid crystal flow
In this paper, we establish some regularity conditions on the density and velocity fields to guarantee the energy conservation of the weak solutions...
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The Existence and Uniqueness of a New Boundary Value Problem (Type of Problem āEā) for a Class of Semi Linear (Power Type Nonlinearities) Mixed Hyperbolic-Elliptic System Equations of Keldysh Type with Changing Time Direction
In present work studied the new boundary value problem for semi linear (Power-type nonlinearities) system equations of mixed hyperbolic -elliptic...
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Entire solutions for some Fermat type functional equations concerning difference and partial differential in ā2
The main purpose of this paper is concerned with the existence and the forms of transcendental entire solutions of several Fermat type functional...
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A Blow-Up Criterion of Strong Solutions to the Quantum Hydrodynamic Model
In this article, we focus on the short time strong solution to a compressible quantum hydrodynamic model. We establish a blow-up criterion about the...
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Analytical Smoothing Effect of Solution for the Boussinesq Equations
In this article, we study the analytical smoothing effect of Cauchy problem for the incompressible Boussinesq equations. Precisely, we use the...
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A mixed hyperbolic-parabolic system to describe predator-prey dynamics
Following [2], a model aiming at the description of two competing populations is introduced. In particular, it is considered a nonlinear system...
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Weak continuity and compactness for nonlinear partial differential equations
This paper presents several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations,...
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Topological arguments for an elliptic equation involving the fractional Laplacian
In this paper, we consider a fractional Nirenberg-type problem involving Ļ -exponent of the Laplacian on the standard n -dimensional spheres
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The Riemann-Hilbert problem for mixed complex equations of first order with degenerate rank 0
This article deals with the Riemann-Hilbert boundary value problem for quasilinear mixed (ellipti-chyperbolic) complex equations of first order with...
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Effect of intrinsic rotations, microstructural expansion and contractions in initial boundary value problem of thermoelastic bodies
This study is dedicated to some basic theorems in the thermoelastodynamics of microstretch bodies. Our intention is to show that the presence of the...
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Multidimensional Conservation Laws: Overview, Problems, and Perspective
Some of recent important developments are overviewed, several longstanding open problems are discussed, and a perspective is presented for the...