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Measure Differential Equations with a General Nonlocal Condition
This paper is devoted to study the existence of solutions for a class of measure differential equations –abbreviated, MDEs– with a general nonlocal...
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Nonlinear Schrödinger equation with nonzero boundary conditions revisited: Dbar approach
The Dbar dressing method is extended to study the focusing/defocusing nonlinear Schrödinger (NLS) equation with nonzero boundary condition. A special...
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Naimark Problem for a Fractional Ordinary Differential Equation
AbstractFor a fractional ordinary differential equation, we consider a problem where the boundary conditions are given in the form of linear...
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Parareal Algorithms for the Cahn-Hilliard Equation
In this work we are interested in designing time parallel algorithm for the Cahn-Hilliard (CH) equation.
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The Hilbert Problem in a Half-plane for Generalized Analytic Functions with a Super-singular Point on the Contour of the Boundary Condition
AbstractIn this paper, we study an inhomogeneous Hilbert boundary value problem with a finite index for one generalized Cauchy–Riemann equation with...
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A mean field type equation on vector bundles
The mean field type equation is a basic problem of mathematics. Up to now, far too little attention has been paid to the mean field type equation on...
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Identification of source term in a nonlinear degenerate parabolic equation with memory
In this work, we consider an inverse backward problem for a nonlinear parabolic equation of the Burgers’ type with a memory term from final data. To...
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The Problem in the Unbounded Domain with the Frankl Condition on the Segment of the Degeneration Line and with a Missing Gellerstedt Condition for a Class of Mixed-Type Equations
AbstractIn an unbounded domain, for a class of equations of mixed type with a singular coefficient, the correctness of the problem is studied in...
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Multi-Soliton Solutions for the Nonlocal Kundu-Nonlinear Schrödinger Equation with Step-Like Initial Data
We investigate the multi-soliton solutions for the Cauchy problem of the nonlocal Kundu-nonlinear Schrödinger (NK-NLS) equation with step-like...
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Navier–Stokes Equations with Regularized Directional Boundary Condition
We consider the steady Navier–Stokes equations in a bounded domain...
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Boundary and Extremum Problems for the Nonlinear Reaction–Diffusion–Convection Equation under the Dirichlet Condition
AbstractThe global solvability of a boundary value problem for the reaction–diffusion–convection equation in which the reaction coefficient...
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Initial-Boundary Value Problems with Generalized Samarskii–Ionkin Condition for Parabolic Equations with Arbitrary Evolution Direction
We study the solvability of boundary value problems nonlocal with respect to the spatial variable with the generalized Samarskii–Ionkin condition for...
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Nonlinear Perturbed BLMP Equation
In the present paper we consider the non-existence of weak solutions related to a class of differential equations connected with the Airy operator....
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On the global existence and analyticity of the mild solution for the fractional Porous medium equation
In this research article we focus on the study of existence of global solution for a three-dimensional fractional Porous medium equation. The main...
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On the Cahn–Hilliard equation with no-flux and strong anchoring conditions
The Cahn–Hilliard equation is a common model to describe phase separation processes of a mixture of two components. We study the Cahn–Hilliard...
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Dynamic of the nonclassical diffusion equation with memory
In this paper, we consider the nonclassical diffusion equation with memory and the nonlinearity of the polynomial growth condition of arbitrary order...
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The Laplace Equation in the Half-Space Involving Nonlinearities Without the Ambrosetti and Rabinowitz Condition
This work establishes the existence of solution for a class of problems that addresses the Laplacian operator in the Euclidean half-space with a...
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Uniform Large Deviations for Stochastic Generalized Burgers-Huxley Equation Driven by Multiplicative Noise
In this paper, we establish a Freidlin-Wentzell type large deviation principle uniformly with respect to initial condition in bounded subsets, that...
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On the isospectral problem of the Camassa–Holm equation
In this paper, we study an isospectral problem of a weighted Sturm–Liouville equation with the Dirichlet boundary condition, which lies at the basis...