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Stochastic Hyperbolic and Parabolic Partial Differential Equations. [PDF]

, 1994
Abstract : The primary objective was to understand fundamental properties of stochastic partial differential equations. The main results obtained concern properties of level sets of the solution of the one-dimensional wave equation, and regularity properties of the two-dimensional wave equation driven by non-white Gaussian noise.
Robert C. Dalang, N. E. Frangos
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Method of Lines for Parabolic Partial Differential Equations

2010
Mathematical modeling of mass or heat transfer in solids involves Fick’s law of mass transfer or Fourier’s law of heat conduction. Engineers are interested in the distribution of heat or concentration across the slab or the material in which the experiment is performed. This process is usually time varying and eventually reaches a steady state.
Ralph E. White, Venkat R. Subramanian
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Computational study for a class of time-dependent singularly perturbed parabolic partial differential equation through tension spline

Computational and Applied Mathematics, 2020
P. M. Kumar, A. Kanth
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A Bifurcation Problem for a Nonlinear Partial Differential Equation of Parabolic Type.

, 1974
We Consider the boundary value problem [d] Here λ is a non negative parameter; f is a given real valuede function defined and a class C2 [d] is an arbitrarily specified function of class C1 on [0, n] satisfying [d] = 0.
N. Chafee, E. Infante
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Parabolic Partial Differential Equations with Nonlocal Initial and Boundary Values

, 2015
Parabolic partial differential equations possessing nonlocal initial and boundary specifications are used to model some real-life applications. This paper focuses on constructing fast and accurate analytic approximations via an easy, elegant and powerful
M. Turkyilmazoglu
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A Priori Regularity of Parabolic Partial Differential Equations

2018
In this thesis, we consider parabolic partial differential equations such as the heat equation, the Fokker-Planck equation, and the porous media equation. Our aim is to develop methods that provide a priori estimates for solutions with singular initial data. These estimates are obtained by understanding the time decay of norms of solutions.
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Controllability for Partial Differential Equations of Parabolic Type

SIAM Journal on Control, 1974
The purpose of this paper is to study questions regarding controllability for the distributed-parameter systems described by partial differential equations of parabolic type. Fattorini [2]–[4] studied controllability by finitely many functions of time.
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Inverse Problems for Parabolic Partial Differential Equations

1986
A simple strategy for dealing with “small” inverse problems is proposed. A keypoint of this strategy is the treatment of the direct problem in the weak setting, employing the strategy of judicious choosing of test functions in order to extract detailed information regarding the properties of the weak solution.
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Matrix Methods for Parabolic Partial Differential Equations

2009
Many of the problems of physics and engineering that require numerical approximations are special cases of the following second-order linear parabolic differential equation: $$ \begin{array}{*{20}c} {\phi \left( {\rm x} \right)u_t \left( {{\rm x};t} \right)} \hfill & { = \sum\limits_{i = 1}^n {\left( {K_i \left( {\rm x} \right)u_{x_i } } \right)_ ...
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On the Theoretical and Numerical Control of a One-Dimensional Nonlinear Parabolic Partial Differential Equation

Journal of Optimization Theory and Applications, 2017
E. Fernández-Cara, Dany Nina-Huamán, Miguel Roberto Nuñez Chávez, Franciane B. Vieira   +3 more
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