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Regularity Results for Nonlocal Evolution Venttsel’ Problems
We consider parabolic nonlocal Venttsel’ problems in polygonal and piecewise smooth two-dimensional domains and study existence, uniqueness and...
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A Remark on Large Time Asymtotics for Solutions of a Nonhomogeneous Viscous Burgers Equation
The existence, uniqueness and regularity of solutions to the Cauchy problem posed for a nonhomogeneous viscous Burger’s equation were shown in Chung,...
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Green Function of the First Boundary-Value Problem for the Fractional Diffusion-Wave Equation in a Multidimensional Rectangular Domain
In this paper, the Green functions of the first boundary-value problem for the fractional diffusion-wave equation in multidimensional (bounded and...
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Solvability of a nonlinear parabolic problem arising in modeling surface reactions
We investigate the existence, uniqueness, and long-time behavior of classical solutions to a coupled system of seven nonlinear parabolic equations....
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Existence and Instability of Some Nontrivial Positive Steady States for the SKT Model with Double Cross Diffusion
This paper is concerned with the nonconstant positive steady states of the Shigesada-Kawasaki-Teramoto model for two competing species with double...
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Simultaneous identification of initial value and source strength in a transmission problem for a parabolic equation
We are concerned with an inverse problem of simultaneously recovering the initial value and source strength in a transmission problem for a parabolic...
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On a New Type of Periodic Fronts in Burgers Type Equations with Modular Advection
A new class of singularly perturbed parabolic periodic boundary value problems for Burgers type equations with modular advection is considered. The...
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A Free Boundary Problem for Some Modified Predator-Prey Model in a Higher Dimensional Environment
We focus on the free boundary problems for a Leslie-Gower predator-prey model with radial symmetry in a higher dimensional environment that is...
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Robust space-time finite element methods for parabolic distributed optimal control problems with energy regularization
As in our previous work ( SINUM 59(2):660–674, 2021) we consider space-time tracking optimal control problems for linear parabolic initial boundary...
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Gevrey Problem for a Mixed Parabolic Equation with a Singular Coefficient
In this paper, we examine the unique solvability of the Gevrey problem for a mixed parabolic equation with singular coefficients in a band. We prove...
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Boundedness and Exponential Stabilization in a Parabolic-Elliptic Keller—Segel Model with Signal-Dependent Motilities for Local Sensing Chemotaxis
In this paper we consider the initial Neumann boundary value problem for a degenerate Keller—Segel model which features a signal-dependent...
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A Refined Green’s Function Estimate of the Time Measurable Parabolic Operators with Conic Domains
We present a refined Green’s function estimate of the time measurable parabolic operators on conic domains that involves mixed weights consisting of...
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New conditions for pattern solutions of a Brusselator model
This paper is devoted to establishing a critical value of the concentration of one intermediary reactant which determines whether pattern solutions...
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The Neumann Problem for Parabolic Hessian Quotient Equations
In this paper, we consider the Neumann problem for parabolic Hessian quotient equations. We show that the k -admissible solution of the parabolic...
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Regularity of Global Attractor for Atmospheric Circulation Equations with Humidity Effect
In this article, regularity of the global attractor for atmospheric circulation equations with humidity effect is considered. It is proved that...
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On fluorescence imaging: The diffusion equation model and recovery of the absorption coefficient of fluorophores
To quantify fluorescence imaging of biological tissues, we need to solve an inverse problem for the coupled radiative transfer equations which...
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A wavelet-in-time, finite element-in-space adaptive method for parabolic evolution equations
In this work, an r -linearly converging adaptive solver is constructed for parabolic evolution equations in a simultaneous space-time variational...
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On Fluorophore Imaging by Diffusion Equation Model: Decompositions and Optimizations
Fluorescence imaging is a target-specific molecular imaging technology using absorption coefficient of fluorophore. For this imaging model governed...