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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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Three-Dimensional Initial-Boundary Value Problem for a Parabolic-Hyperbolic Equation with a Degenerate Parabolic Part
AbstractAn initial-boundary value problem is studied for a nonhomogeneous equation of mixed parabolic-hyperbolic type in three variables with a...
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The Cost of Null Controllability for a Backward Stochastic Degenerate Parabolic Equation in the Vanishing Viscosity Limit
In this paper, we investigate the cost of null controllability for a backward stochastic degenerate parabolic equation with a boundary control in the...
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Inverse Problems of Finding the Lower Term in a Multidimensional Degenerate Parabolic Equation
We study the inverse problem of recovering the lower term of a degenerate parabolic equation with many spatial variables under an additional integral...
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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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Dynamical behavior of a degenerate parabolic equation with memory on the whole space
This paper is concerned with the existence and uniqueness of global attractors for a class of degenerate parabolic equations with memory on
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Boundary controllability for a 1D degenerate parabolic equation with drift, a singular potential, and a Neumann boundary condition
We prove the null controllability of a one-dimensional degenerate parabolic equation with drift and a singular potential. Here, we consider a...
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On the Structure of Entropy Solutions to the Riemann Problem for a Degenerate Nonlinear Parabolic Equation
We find an explicit form of entropy solution to a Riemann problem for a degenerate nonlinear parabolic equation with piecewise constant velocity and...
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Carleman estimate and null controllability for a degenerate parabolic equation with a slightly superlinear reaction term
This paper concerns the null controllability of an one-dimensional degenerate parabolic equation with a slightly superlinear reaction term in a...
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Well-posedness and longtime dynamics for the finitely degenerate parabolic and pseudo-parabolic equations
We consider the initial-boundary value problem for degenerate parabolic and pseudo-parabolic equations associated with Hörmander-type operator. Under...
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Periodic solutions for a degenerate double-phase parabolic equation with variable growth
The purpose of this work is the investigation of a degenerate parabolic equation with double-phase operator, variable growth and strongly nonlinear...
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Local Boundary Value Problems for a Degenerate Loaded Equation of Parabolic-Hyperbolic Type of the Second Kind
AbstractIn the present paper, we pose and study local boundary value problems for a parabolic-hyperbolic equation of the second kind with...
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An energy formula for fully nonlinear degenerate parabolic equations in one spatial dimension
Energy (or Lyapunov) functions are used to prove stability of equilibria, or to indicate a gradient-like structure of a dynamical system. Matano...
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Solvability of a Family of Nonlinear Degenerate Parabolic Mixed Equations
In this paper, we show an abstract setting for analyzing the solvability of a class of nonlinear mixed degenerate parabolic equations. Specifically,...
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Fundamental Solutions for Degenerate Parabolic Equations: Existence, Properties, and some Applications
We propose overview of the results of construction, research, and applications of fundamental solutions of the Cauchy problem for several classes of...
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Observability Inequality from Measurable Sets for Degenerate Parabolic Equations and its Applications
In this study, we employ the established Carleman estimates and propagation estimates of smallness from measurable sets for real analytic functions,...
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On Fundamental Solutions and Gaussian Bounds for Degenerate Parabolic Equations with Time-dependent Coefficients
We consider second order degenerate parabolic equations with real, measurable, and time-dependent coefficients. We allow for degenerate ellipticity...
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Numerical analysis of nonlinear degenerate parabolic problems with application to eddy current models
This paper deals with the numerical analysis for a family of nonlinear degenerate parabolic problems. The model is spatially discretized using a...
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High-order weighted compact nonlinear scheme for solving degenerate parabolic equations
Solutions of the nonlinear degenerate parabolic equations may be discontinuous. The classical numerical schemes cannot well handle such...
