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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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A heat equation approach to intertwining
In this paper we present anew approach based on the heat equation and extension problems to some intertwining formulas arising in conformal CR...
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Localized Sequential Bubbling for the Radial Energy Critical Semilinear Heat Equation
In this expository note, we prove a localized bubbling result for solutions of the energy critical nonlinear heat equation with bounded
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The Heat Equation with Singular Potentials. II: Hypoelliptic Case
In this paper we consider the heat equation with a strongly singular potential and show that it has a very weak solution. Our analysis is devoted to...
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A robust stability criterion on the time-conformable fractional heat equation in a axisymmetric cylinder
In this paper we consider a time-conformable fractional heat equation that admits heat sources that belong to a prefixed set of functions. Assuming...
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On the loss of mass for the heat equation in an exterior domain with general boundary conditions
In this work, we study the decay of mass for solutions to the heat equation in exterior domains, i.e., domains which are the complement of a smooth...
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Lebeau–Robbiano Inequality for Heat Equation with Dynamic Boundary Conditions and Optimal Null Controllability
The paper deals with time and norm optimal control problems for the heat equation with dynamic boundary conditions in the context of the null...
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Blow-up of nonnegative solutions of an abstract semilinear heat equation with convex source
We give a sufficient condition for non-existence of global nonnegative mild solutions of the Cauchy problem for the semilinear heat equation
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Existence of Regular Solutions for a Class of Incompressible Non-Newtonian MHD Equations Coupled to the Heat Equation
We consider a system of PDE’s describing the steady flow of an electrically conducting fluid in the presence of a magnetic field. The system of...
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A nonlinear stochastic heat equation with variable thermal conductivity and multiplicative noise
We consider a stochastic heat equation with variable thermal conductivity, on infinite domain, with both deterministic and stochastic source and with...
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On the Controllability of a Free-Boundary Problem for 1D Heat Equation with Local and Nonlocal Nonlinearities
This paper deals with the analysis of the internal control of a free-boundary problem for the 1D heat equation with local and nonlocal...
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Fractional heat equation with singular nonlinearity
Our aim in this paper is to analyze the existence and regularity of solutions for the following nonlocal parabolic problem involving the fractional...
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Insensitizing Controls of a 1D Stefan Problem for the Semilinear Heat Equation
This paper deals with the existence of insensitizing controls for a 1D free-boundary problem of the Stefan kind for a semilinear PDE. The...