scholarly journals On Time Periodic Solutions of the Dirichlet Problem for Degenerate Parabolic Equations of Nondivergence Type

1996 ◽  
Vol 201 (2) ◽  
pp. 396-416 ◽  
Author(s):  
Yoshikazu Giga ◽  
Noriko Mizoguchi
Keyword(s):  
Dirichlet Problem ◽  
Periodic Solutions ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equations ◽  
Time Periodic Solutions ◽  
Degenerate Parabolic ◽  
Time Periodic

scholarly journals Cauchy-Dirichlet problem for the nonlinear degenerate parabolic equations

2005 ◽  
Vol 2005 (6) ◽  
pp. 607-617 ◽  
Author(s):  
Ismail Kombe
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dirichlet Problem ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equations ◽  
Parabolic Partial Differential Equation ◽  
Nonlinear Parabolic ◽  
Nonlinear Degenerate Parabolic Equations ◽  
Degenerate Parabolic ◽  
Nonlinear Degenerate

We will investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation:∂u/∂t=ℒu+V(w)up−1inΩ×(0,T),1<p<2,u(w,0)=u0(w)≥0inΩ,u(w,t)=0on∂Ω×(0,T)whereℒis the subellipticp-Laplacian andV∈Lloc1(Ω).

Time-periodic solutions to semilinear parabolic equations

1986 ◽  
Vol 104 (3-4) ◽  
pp. 329-342 ◽  
Author(s):  
Peter Grindrod ◽  
Bryan P. Rynne
Keyword(s):  
Periodic Solutions ◽  
Parabolic Equations ◽  
Evolution Equations ◽  
Periodic Forcing ◽  
Linear Diffusion ◽  
Linear Evolution ◽  
Time Periodic Solutions ◽  
Semilinear Parabolic ◽  
Time Periodic ◽  
Linear Evolution Equations

SynopsisWe consider a class of non-linear evolution equations subject to a periodic forcing term. Using bifurcation theory we obtain results on the existence and number of periodic solutions. The theory applies to semi-linear diffusion equations defined on bounded or unbounded domains.

Coexistence Solutions for a Periodic Competition Model with Singular–Degenerate Diffusion

2016 ◽  
Vol 60 (4) ◽  
pp. 1065-1075
Author(s):  
Yifu Wang ◽  
Jingxue Yin ◽  
Yuanyuan Ke
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Parabolic Equations ◽  
Competition Model ◽  
Degenerate Parabolic Equations ◽  
Degenerate Diffusion ◽  
Volterra Type ◽  
Non Local ◽  
Degenerate Parabolic

AbstractWe investigate a system of singular–degenerate parabolic equations with non-local terms, which can be regarded as a spatially heterogeneous competition model of Lotka–Volterra type. Applying the Leray–Schauder fixed-point theorem, we establish the existence of coexistence periodic solutions to the problem, which, together with the existing literature, gives a complete picture for such a system for all parameters.

scholarly journals A Two-Species Cooperative Lotka-Volterra System of Degenerate Parabolic Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Jiebao Sun ◽  
Dazhi Zhang ◽  
Boying Wu
Keyword(s):  
Parabolic Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Volterra Model ◽  
Generalized Solutions ◽  
Degenerate Parabolic Equations ◽  
Volterra System ◽  
Degenerate Parabolic ◽  
Initial Boundary Value ◽  
Time Periodic

We consider a cooperating two-species Lotka-Volterra model of degenerate parabolic equations. We are interested in the coexistence of the species in a bounded domain. We establish the existence of global generalized solutions of the initial boundary value problem by means of parabolic regularization and also consider the existence of the nontrivial time-periodic solution for this system.

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