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An adaptive certified space-time reduced basis method for nonsmooth parabolic partial differential equations
In this paper, a nonsmooth semilinear parabolic partial differential equation (PDE) is considered. For a reduced basis (RB) approach, a space-time...
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THE DUAL RECIPROCITY BOUNDARY ELEMENT METHOD FOR ONE-DIMENSIONAL NONLINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS
This article describes a numerical method based on the dual reciprocity boundary element method (DRBEM) for solving some well-known nonlinear...
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A fast Galerkin-spectral method based on discrete Legendre polynomials for solving parabolic differential equation
The goal of this investigation is to achieve the numerical solution of a two-dimensional parabolic partial differential equation(PDE). The proposed...
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Quasi Solution of an Inverse Fractional Stochastic Nonlinear Partial Differential Equation of Parabolic Type
In this paper, the existence theorem for a quasi solution of an inverse fractional stochastic parabolic equation driven by multiplicative noise in...
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A comparison principle for doubly nonlinear parabolic partial differential equations
In this paper, we derive a comparison principle for non-negative weak sub- and super-solutions to doubly nonlinear parabolic partial differential...
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Partial Differential Equations I Basic Theory
The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism,...
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Partial Differential Equations An Introduction to Analytical and Numerical Methods
This textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two...
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About mean value theorems for the singular parabolic equation
A huge number of physical, geometric, and probabilistic problems lead to the construction and study of parabolic partial differential equations. The...
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An Actuated Computational Method for Treating Parabolic Partial Delay Integro-Differential Equations Constrained by Infinite Boundary
For the first time via this study, the ultimate effort is inclined to numerically solve one-dimensional parabolic partial integro-differential...
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Uniformly convergent finite difference methods for singularly perturbed parabolic partial differential equations with mixed shifts
In this paper, exponentially fitted finite difference methods are presented for singularly perturbed one-dimensional parabolic partial differential...
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Group classification for one type of space-time fractional quasilinear parabolic equation
In this paper, we present the Lie symmetry analysis for the space-time fractional quasilinear parabolic equation. A group classification is then...
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On Approximate Matrix Factorization and TASE W-Methods for the Time Integration of Parabolic Partial Differential Equations
Linearly implicit methods for Ordinary Differential Equations combined with the application of Approximate Matrix Factorization (AMF) provide...
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A Quasi Solution for a Nonlinear Inverse Stochastic Partial Differential Equation of Parabolic Type
This paper concerns a nonlinear inverse stochastic parabolic partial differential equation. The source term of this problem consists branches of...
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Multiperiodic Solution of the Initial-Boundary Value Problem for an Integro-Differential Equation of the Parabolic Type
AbstractThis paper investigates the initial-boundary value problem for an integro-differential equation of parabolic type with a differentiation...
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How Much Can One Learn a Partial Differential Equation from Its Solution?
In this work, we study the problem of learning a partial differential equation (PDE) from its solution data. PDEs of various types are used to...
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Blow-Up Phenomena for a Sixth-Order Partial Differential Equation with a General Nonlinearity
In this paper, we study the blow-up results for the sixth-order time-dependent partial differential equation (PDE). First, we establish the existence...
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On the Small Time Asymptotics of Quasilinear Parabolic Stochastic Partial Differential Equations
In this paper, we establish small time large deviation principles for the quasilinear parabolic stochastic partial differential equations with...
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Mixed Problem for a Nonlinear Parabolic Equation with Involution
AbstractIn this paper, we consider a nonlinear parabolic differential equation with involution. With respect to spatial variable is used Dirichlet...