12 Result(s)
within
J. R. CANNON
Mathematics
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Chapter
The Approximation of Harmonic and Parabolic Functions on Half-Spaces from Interior Data
The object of this paper is to discuss the numerical approximation of functions either harmonic or parabolic in a half-space given the approximate values of the functions on some subset of the open half-space....
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Chapter
Identifying a Time Dependent Unknown Coefficient in a Nonlinear Heat Equation
In this paper we show how an unknown coefficient inverse problem may be reformulated as a problem involving a trace type functional partial differential equation. The trace type functional problem can be solve...
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Article
Galerkin methods and L2-error estimates for hyperbolic integro-differential equations
In this paper we shall study Galerkin approximations to the solution of linear second-order hyperbolic integro-differential equations. The continuous and Crank-Nicolson discrete time Galerkin procedures will b...
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Article
Non-classicalH 1 projection and Galerkin methods for non-linear parabolic integro-differential equations
In this paper the Galerkin method is analyzed for the following nonlinear integro-differential equation of parabolic type: $$c(u)u_t ...
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Chapter and Conference Paper
The initial value problem for the Boussinesq equations with data in Lp
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Article
A Galerkin procedure for systems of differential equations
A continuous time and an extrapolated coefficient Crank-Nicolson-Galerkin method are considered for approximating solutions of boundary and initial value problems for a quasi-linear parabolic system of partial...
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Article
A numerical experiment on the determination of kinetic rate constants in the presence of diffusion
Two chemicals,A andB, are allowed to diffuse together and a reaction described by $$A + B\mathop \rightleftharpoons \limits_{K_{ - 1}...
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Article
A two phase stefan problem: regularity of the free boundary
Con riferimento ad un problema di Stefan a due fasi in uno strato piano indefinito, viene dimostrata la infinita differenziabilità della funzione x=s(t) che rappresenta ad ogni istante la ascissa del piano di ...
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Article
Determination of an unknown forcing function in a hyperbolic equation from overspecified data
The determination of a forcing function depending only upon the space variable in a hyperbolic equation is achieved by the over-specification of the bouudary data. The problem is an example of a not-well posed...
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Article
A Cauchy problem for the heat equation
Let u(x, t) satisfy the heat equation in 0<x<1, 0<t≤T. Let u(x, 0)=0 for 0<x<1 and let |u(0, t)|<ε, | ux(0, t) |<ε, and | u(1, t) |<M for 0≤t≤T. Then, ...
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Article
A priori estimate for continuation of the solution of the heat equation in the space variable
Let u(x, t) satisfy the heat equation in a region D in the x−t plane and vanish initially. Let |u|<M0 in D and |u i 2 |<∈ in D* ⊂ D. Then, in D−D*, |u|< ...
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Article
A dirichlet problem for an equation of mixed type with a discontinuous coefficient
A Dirichlet problem for an equation of mixed type with a discontinuous coefficient is considered for a rectangle. In one part of the rectangle, Laplace's equation is specified while the wave equation is specif...
