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Mixed Problem for a Higher-Order Nonlinear Pseudoparabolic Equation
We examine the unique generalized solvability of the mixed problem for a higher-order nonlinear pseudoparabolic equation with two parameters in mixed...
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Global solutions to 1D compressible Navier-Stokes/Allen-Cahn system with density-dependent viscosity and free-boundary
This paper is concerned with the Navier-Stokes/Allen-Cahn system, which is used to model the dynamics of immiscible two-phase flows. We consider a 1D...
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Global Solutions and Interactions of Non-selfsimilar Elementary Waves for n-D Non-homogeneous Burgers Equation
We investigate the global structures of the non-selfsimilar solutions for n -dimensional ( n -D) non-homogeneous Burgers equation, in which the initial...
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On Features of the Solution of a Boundary-Value Problem for the Multidimensional Integro-Differential Benney–Luke Equation with Spectral Parameters
In this paper, we consider the problems on the solvability and constructing solutions of one nonlocal boundary-value problem for the...
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On the determination of the spatial-dependent potential coefficient in a linear pseudoparabolic equation
We consider the determination of an unknown spatial-dependent coefficient for the pseudoparabolic system with Dirichlet boundary condition from...
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The Uniqueness of the Lp Minkowski Problem for q-Torsional Rigidity
In this paper, we prove the uniqueness of the L p Minkowski problem for q -torsional rigidity with p > 1 and q > 1 in smooth case. Meanwhile, the L p ...
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Weak-strong uniqueness for three dimensional incompressible active liquid crystals
The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models. In this...
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Existence and uniqueness for a two-dimensional Ventcel problem modeling the equilibrium of a prestressed membrane
This paper deals with a mixed boundary-value problem of Ventcel type in two variables. The peculiarity of the Ventcel problem lies in the fact that...
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Determining of Coefficients and the Classical Solvability of a Nonlocal Boundary-Value Problem for the Benney–Luke Integro-Differential Equation with Degenerate Kernel
Using the Fourier method of separation of variables, we examine the classical solvability and construct solutions of a nonlocal inverse...
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Strong unique continuation property for a class of fourth order elliptic equations with strongly singular potentials
In this paper we prove the strong unique continuation property for a class of fourth order elliptic equations involving strongly singular potentials....
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On the Relation Between the Girsanov Transform and the Kolmogorov Equations for SPDEs
The Girsanov transform and Kolmogorov equations are two useful methods for studying SPDEs. It is shown that, under suitable conditions, the series...
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Kinetic BGK Model for a Crowd: Crowd Characterized by a State of Equilibrium
This article focuses on dynamic description of the collective pedestrian motion based on the kinetic model of Bhatnagar-Gross-Krook. The proposed...
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The Regularity and Uniqueness of a Global Solution to the Isentropic Navier-Stokes Equation with Rough Initial Data
A global weak solution to the isentropic Navier-Stokes equation with initial data around a constant state in the L 1 ∩ BV class was constructed in...
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On a Boundary-Value Problem for a Fourth-Order Partial Integro-Differential Equation with Degenerate Kernel
In this paper, the classical solvability of a nonlocal boundary-value problem for a three dimensional, homogeneous, fourth-order, pseudoelliptic...
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Unconditional uniqueness of higher order nonlinear Schrödinger equations
We show the existence of weak solutions in the extended sense of the Cauchy problem for the cubic fourth order nonlinear Schrödinger equation with...
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Weak-Strong Uniqueness for Navier-Stokes/Allen-Cahn System
The coupled Navier-Stokes/Allen-Cahn system is a simple model to describe phase separation in two-component systems interacting with an...
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Well-posedness to 3D Burgers’ equation in critical Gevrey Sobolev spaces
We prove that the three-dimensional periodic Burgers’ equation has a unique global in time solution in a critical Gevrey–Sobolev space. Comparatively...