systems of parabolic equations
Recently Published Documents


TOTAL DOCUMENTS

32
(FIVE YEARS 1)

H-INDEX

6
(FIVE YEARS 0)

Author(s):  
Alexander Dobrick ◽  
Jochen Glück

AbstractWhen we are interested in the long-term behaviour of solutions to linear evolution equations, a large variety of techniques from the theory of $$C_0$$ C 0 -semigroups is at our disposal. However, if we consider for instance parabolic equations with unbounded coefficients on $${\mathbb {R}}^d$$ R d , the solution semigroup will not be strongly continuous, in general. For such semigroups many tools that can be used to investigate the asymptotic behaviour of $$C_0$$ C 0 -semigroups are not available anymore and, hence, much less is known about their long-time behaviour. Motivated by this observation, we prove new characterisations of the operator norm convergence of general semigroup representations—without any time regularity assumptions—by adapting the concept of the “semigroup at infinity”, recently introduced by M. Haase and the second named author. Besides its independence of time regularity, our approach also allows us to treat the discrete-time case (i.e. powers of a single operator) and even more abstract semigroup representations within the same unified setting. As an application of our results, we prove a convergence theorem for solutions to systems of parabolic equations with the aforementioned properties.



2020 ◽  
Vol 28 (6) ◽  
pp. 797-814
Author(s):  
Elena-Alexandra Melnig

AbstractWe consider systems of parabolic equations coupled in zero and first order terms. We establish Lipschitz estimates in {L^{q}}-norms, {2\leq q\leq\infty}, for the source in terms of the solution in a subdomain. The main tool is a family of appropriate Carleman estimates with general weights, in Lebesgue spaces, for nonhomogeneous parabolic systems.



2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Sen Zhou

Abstract In this paper, we study a coupled systems of parabolic equations subject to large initial data. By using comparison principle and Kaplan’s method, we get the upper and lower bound for the life span of the solutions.



2018 ◽  
Vol 18 (2) ◽  
pp. 195-215
Author(s):  
Giovanni Vidossich

Abstract We present existence and multiplicity theorems for periodic mild solutions to parabolic evolution equations. Their peculiarity is a link with the spectrum of the generator of the semigroup rather than with the spectrum of the linearized periodic BVP for the evolution equation. They provide a positive solution to the open problem risen by Becker [3], they extend some results of Castro and Lazer [5] from scalar to systems of parabolic equations, and they are new even for finite-dimensional ODEs.



2018 ◽  
Vol 8 (3) ◽  
pp. 777-787
Author(s):  
Cătălin-George Lefter ◽  
◽  
Elena-Alexandra Melnig


2015 ◽  
Vol 17 (6) ◽  
pp. 2105-2114 ◽  
Author(s):  
A. Carrasco ◽  
Hugo Leiva ◽  
N. Merentes ◽  
J. L. Sanchez










Sign in / Sign up

Export Citation Format

Share Document