scholarly journals On well-posedness of semilinear parabolic and elliptic problems in the hyperbolic space

2011 ◽  
Vol 251 (7) ◽  
pp. 1972-1989 ◽  
Author(s):  
Fabio Punzo
Keyword(s):  
Hyperbolic Space ◽  
Elliptic Problems ◽  
Well Posedness ◽  
Semilinear Parabolic

scholarly journals Space-Time Estimates of Mild Solutions of a Class of Higher-Order Semilinear Parabolic Equations in Lp

2014 ◽  
Vol 1 (1) ◽  
Author(s):  
Albert N. Sandjo ◽  
Célestin Wafo Soh
Keyword(s):  
Thin Film ◽  
Epitaxial Growth ◽  
Parabolic Equations ◽  
Mild Solutions ◽  
Film Theory ◽  
Well Posedness ◽  
Semilinear Parabolic Equations ◽  
Unified Framework ◽  
Time Estimates ◽  
Semilinear Parabolic

AbstractWe establish the well-posedness of boundary value problems for a family of nonlinear higherorder parabolic equations which comprises some models of epitaxial growth and thin film theory. In order to achieve this result, we provide a unified framework for constructing local mild solutions in C

A note on positivity of two-dimensional differential operators

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4651-4663 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Sema Akturk
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Half Plane ◽  
Differential Operators ◽  
Elliptic Problems ◽  
Well Posedness ◽  
Two Dimensional ◽  
Ellipticity Condition ◽  
Fractional Spaces ◽  
Uniform Ellipticity

We consider the two-dimensional differential operator A(t,x)u(t,x) = -a11 (t, x) utt -a22(t,x)uxx +?u defined on functions on the half-plane R+ x R with the boundary condition u(0,x) = 0, x ? R where aii(t,x), i = 1,2 are continuously differentiable and satisfy the uniform ellipticity condition a2 11(t,x) + a222(t,x)? ? > 0, ? > 0. The structure of fractional spaces E?,1 (L1 (R+ x R), A(t,x)) generated by the operator A(t,x) is investigated. The positivity of A(t,x) in L1 (W2?1(R+ x R)) spaces is established. In applications, theorems on well-posedness in L1 (W2?1 (R+ x R)) spaces of elliptic problems are obtained.

scholarly journals Differential Harnack Estimates for a Semilinear Parabolic System

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Hui Wu
Keyword(s):  
Hyperbolic Space ◽  
Positive Solutions ◽  
Parabolic System ◽  
Space Time ◽  
Harnack Inequalities ◽  
Harnack Estimates ◽  
Semilinear Parabolic System ◽  
Semilinear Parabolic

In this paper, we prove differential Harnack inequalities for positive solutions of a semilinear parabolic system on hyperbolic space. We use the inequalities to construct classical Harnack estimates by integrating along space-time.

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