An Analytic Semigroup Associated to a Degenerate Evolution Equation

2020 ◽  
pp. 85-100
Author(s):  
Angelo Favini ◽  
Jerome A. Goldstein ◽  
Silvia Romanelli
Keyword(s):  
Evolution Equation ◽  
Analytic Semigroup ◽  
Degenerate Evolution Equation

scholarly journals On a Nonlinear Degenerate Evolution Equation with Nonlinear Boundary Damping

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
A. T. Lourêdo ◽  
G. Siracusa ◽  
C. A. Silva Filho
Keyword(s):  
Evolution Equation ◽  
Global Stability ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Uniqueness Of Solutions ◽  
Boundary Damping ◽  
Degenerate Evolution Equation ◽  
Neumann Type ◽  
Nonlinear Degenerate

This paper deals essentially with a nonlinear degenerate evolution equation of the formKu″-Δu+∑j=1nbj∂u′/∂xj+uσu=0supplemented with nonlinear boundary conditions of Neumann type given by∂u/∂ν+h·, u′=0. Under suitable conditions the existence and uniqueness of solutions are shown and that the boundary damping produces a uniform global stability of the corresponding solutions.

scholarly journals On a nonlinear degenerate evolution equation with strong damping

1992 ◽  
Vol 15 (3) ◽  
pp. 543-552 ◽  
Author(s):  
Jorge Ferreira ◽  
Ducival Carvalho Pereira
Keyword(s):  
Weak Solution ◽  
Evolution Equation ◽  
Bounded Domain ◽  
Real Function ◽  
Smooth Boundary ◽  
Global Weak Solution ◽  
Continuous Real Function ◽  
Strong Damping ◽  
Degenerate Evolution Equation ◽  
Nonlinear Degenerate

In this paper we consider the nonlinear degenerate evolution equation with strong damping,(*)      {K(x,t)utt−Δu−Δut+F(u)=0   in   Q=Ω×]0,T[u(x,0)=u0,   (ku′)(x,0)=0   in   Ωu(x,t)=0           on   ∑=Γ×]0,T[whereKis a function withK(x,t)≥0,K(x,0)=0andFis a continuous real function satisfying(**)     sF(s)≥0,   for   all   s∈R,             Ωis a bounded domain ofRn, with smooth boundaryΓ. We prove the existence of a global weak solution for (*).

Conserved Quantities for the General Linear Heat Equation

2016 ◽  
pp. 4437-4439
Author(s):  
Adil Jhangeer ◽  
Fahad Al-Mufadi
Keyword(s):  
Evolution Equation ◽  
Heat Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Lagrangian Approach ◽  
General Linear ◽  
Conserved Quantities ◽  
Linear Heat ◽  
The Family ◽  
Partial Lagrangian

In this paper, conserved quantities are computed for a class of evolution equation by using the partial Noether approach [2]. The partial Lagrangian approach is applied to the considered equation, infinite many conservation laws are obtained depending on the coefficients of equation for each n. These results give potential systems for the family of considered equation, which are further helpful to compute the exact solutions.

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