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Mixed Problem with Integral Condition for a Loaded Third Order Pseudoparabolic Equation
We consider a nonlocal problem with an integral condition for a loaded third order pseudoparabolic equation in a rectangular domain. We prove the...
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Polynomial Energy Decay Rate for the Wave Equation with Kinetic Boundary Condition
This paper concerns the polynomial decay of the dissipative wave equation subject to Kinetic boundary condition and non-neglected density in the...
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The nonhomogeneous boundary-value problems for the 1D-NLS equation with lineal boundary condition
In this paper, we study the initial-boundary-value problem for the cubic nonlinear Schrödinger equation, formulated on a half-line with different...
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Existence of Solutions for the Laplacian Equation with Exponential Neumann Boundary Condition
In this paper, we consider the Laplacian equation with exponential Neumann boundary condition on a compact Riemann surface Σ with nonempty boundary ∂ Σ...
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Boundary Layer Solution of the Boltzmann Equation for Specular Boundary Condition
In the paper, we establish the existence of steady boundary layer solution of Boltzmann equation with specular boundary condition in L
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Direct and Inverse Initial Boundary Value Problems for Heat Equation with Non-Classical Boundary Condition
AbstractIn this paper we consider solvability of an initial boundary value problem for the heat equation with a dynamic type boundary condition....
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Tricomi Problem for Mixed Parabolic–Hyperbolic Equation with Higher Order Boundary Condition
In this paper, we study an analogue of Tricomi problem for a parabolic–hyperbolic equation. One boundary condition in the parabolic part of the...
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Gellerstedt Problem with a Nonlocal Oddness Boundary Condition for the Lavrent’ev–Bitsadze Equation
AbstractWe study the Gellerstedt problem for the Lavrent’ev–Bitsadze equation with the oddness boundary condition on the boundary of the ellipticity...
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Inverse Source Problem for the Subdiffusion Equation on a Metric Star Graph with Integral Overdetermination Condition
AbstractIn this article, it is investigated the inverse source problem for the subdiffusion equation on the metric star graph in Sobolev space with...
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Homogenization of a Parabolic Equation in a Perforated Domain with a Unilateral Dynamic Boundary Condition: Critical Case
The present paper studies the homogenization of the parabolic equation stated in a domain perforated by “tiny” balls. On the boundary of these...
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Boundary controllability for a 1D degenerate parabolic equation with a Robin boundary condition
In this paper, we prove the null controllability of a one-dimensional degenerate parabolic equation with a weighted Robin boundary condition at the...
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Uniqueness of a nonlinear integro-differential equation with nonlocal boundary condition and variable coefficients
This paper studies the uniqueness of solutions to a two-term nonlinear fractional integro-differential equation with nonlocal boundary condition and...
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Uniqueness of Solution of Boundary-Value Problem with Integral Condition for Mixed-Type Equation with Bessel Operator
AbstractA boundary-value problem with nonlocal integral condition is studied for a mixed-type equation with Bessel operator in a rectangular domain....
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A numerical scheme for a diffusion equation with nonlocal nonlinear boundary condition
In this article, a numerical scheme to find approximate solutions to the McKendrick–Von Foerster equation with diffusion (M-V-D) is presented. This...
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Solution to a Two-Dimensional Nonlinear Parabolic Heat Equation Subject to a Boundary Condition Specified on a Moving Manifold
AbstractThis paper is devoted to the study of a degenerating parabolic heat equation with nonlinearities of a general type in the presence of a...
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Phragmén–Lindelöf theorems for a weakly elliptic equation with a nonlinear dynamical boundary condition
We establish two Phragmén–Lindelöf theorems for a fully nonlinear elliptic equation. We consider a dynamical boundary condition that includes both...
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Heat Transfer Problem for the Boltzmann Equation in a Channel with Diffusive Boundary Condition
In this paper, the authors study the 1D steady Boltzmann flow in a channel. The walls of the channel are assumed to have vanishing velocity and given...
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Linear inverse problems for the heat equation and non-local boundary value problems with generalized Samarskii–Ionkin condition
The paper is devoted to the study of the solvability of linear inverse problems for a one-dimensional heat equation with an unknown right-hand side....
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Sharp Condition for Global Existence of Supercritical Nonlinear Schrödinger Equation with a Partial Confinement
We study the L 2 -supercritical nonlinear Schrödinger equation (NLS) with a partial confinement, which is the limit case of the cigar-shaped model in...
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A necessary and sufficient condition of blow-up for a nonlinear equation
We investigate a nonlinear equation with quadratic nonlinearities, including a nonlinear model in Silva and Freire (J. Differ. Equ. 320:371–398,
2022 )...