Construction of a solution of a quasilinear partial differential equation of parabolic type with oscillating and slowly varying coefficients

1995 ◽  
Vol 47 (8) ◽  
pp. 1290-1298
Author(s):  
S. A. Shchegolev
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Parabolic Type ◽  
Partial Differential ◽  
Varying Coefficients ◽  
Quasilinear Partial Differential Equation

Monotone methods and attractivity results for Volterra integro-partial differential equations

1981 ◽  
Vol 89 (1-2) ◽  
pp. 135-142 ◽  
Author(s):  
Andrea Schiaffino ◽  
Alberto Tesei
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Past History ◽  
Main Tool ◽  
Parabolic Type ◽  
Supremum Norm ◽  
Partial Differential ◽  
Diffusion Effects ◽  
Monotone Methods ◽  
Globally Attractive

SynopsisA Volterra integro-partial differential equation of parabolic type, which describes the time evolution of a population in a bounded habitat, subject both to past history and space diffusion effects, is investigated; general homogeneous boundary conditions are admissible. Under suitable conditions, the unique nontrivial nonnegative equilibrium is shown to be globally attractive in the supremum norm. Monotone methods are the main tool of the proof.

V.—On an Elementary Solution of a Partial Differential Equation of Parabolic Type. Part II: The Nature of the Singularity.

1941 ◽  
Vol 61 (1) ◽  
pp. 54-60 ◽  
Author(s):  
E. T. Copson
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Parabolic Type ◽  
Elementary Solution ◽  
Partial Differential ◽  
Image Position

SummaryIt is shown that the elementary solution Γ(x, ξ; t – τ) of the equationbehaves, as t → τ + O, in very much the same manner as the elementary solution of the equation of heat.

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