Existence and uniqueness of solutions of system governed by second order quasilinear integro-partial differential equation of parabolic type

1979 ◽  
Vol 19 (1) ◽  
pp. 301-302
Author(s):  
K. L. Teo
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Existence And Uniqueness ◽  
Parabolic Type ◽  
Second Order ◽  
Uniqueness Of Solutions ◽  
Partial Differential

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.

XIII.—Partial Differential Equations and the Calculus of Variations

1927 ◽  
Vol 46 ◽  
pp. 126-135 ◽  
Author(s):  
E. T. Copson
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Calculus Of Variations ◽  
Order Equation ◽  
Second Order ◽  
Physical Problem ◽  
Partial Differential ◽  
Hamiltonian Principle

A partial differential equation of physics may be defined as a linear second-order equation which is derivable from a Hamiltonian Principle by means of the methods of the Calculus of Variations. This principle states that the actual course of events in a physical problem is such that it gives to a certain integral a stationary value.

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