Pointwise Bounds and Blow-up for Systems of Semilinear Parabolic Inequalities and Nonlinear Heat Potential Estimates
@article{Ghergu2015PointwiseBA, title={Pointwise Bounds and Blow-up for Systems of Semilinear Parabolic Inequalities and Nonlinear Heat Potential Estimates}, author={Marius Ghergu and Steven D. Taliaferro}, journal={arXiv: Analysis of PDEs}, year={2015} }
Figures from this paper
3 Citations
BLOW-UP VERSUS GLOBAL RADIAL SOLUTION FOR FREE BOUNDARY SYSTEM WITH NONLINEAR INHOMOGENEOUS GRADIENT AND SOURCE TERMS
- Mathematics
- 2022
This paper concerns the characterization of blowup and global radial solutions of a two-free boundaries system read by
On the characterization of Bow-up and Global Radial solution for free boundary system with nonlinear inhomogeneous gradient and source term
- Mathematics
- 2022
. In the recent decade, a lot of attention has been drawn to the question on the global phenomena of free boundary problems. Aiming to understand the blow-up and global phenomena incorporating with…
Representation formulae for nonhomogeneous differential operators and applications to PDEs
- MathematicsJournal of Differential Equations
- 2022
References
SHOWING 1-10 OF 20 REFERENCES
Existence of a stable blow-up profile for the nonlinear heat equation with a critical power nonlinear gradient term
- MathematicsTransactions of the American Mathematical Society
- 2019
We consider the nonlinear heat equation with a nonlinear gradient term: $\partial_t u =\Delta u+\mu|\nabla u|^q+|u|^{p-1}u,\; \mu>0,\; q=2p/(p+1),\; p>3,\; t\in (0,T),\; x\in \R^N.$ We construct a…
Existence and nonexistence of global solutions of degenerate and singular parabolic systems
- Mathematics
- 2000
where p,q > 1 and u(x,0) = u0(x), v(x,0) = v0(x), x ∈ R. Systems like (1.1) and (1.2) will be called degenerate and singular, respectively. Several authors have addressed this problem recently: we…
Elliptic Partial Differential Equations of Second Order
- Mathematics
- 1997
We study in this chapter a class of partial differential equations that generalize and are to a large extent represented by Laplace’s equation. These are the elliptic partial differential equations…
A Liouville theorem and blowup behavior for a vector‐valued nonlinear heat equation with no gradient structure
- Mathematics
- 2001
We prove a Liouville Theorem for the following heat system whose nonlinearity has no gradient structure ∂tu = ∆u + v p , ∂tv = ∆v + u q , where pq > 1, p ≥ 1, q ≥ 1 and |p − q| small. We then deduce…
Sobolev Spaces: with Applications to Elliptic Partial Differential Equations
- Mathematics
- 2011
Sobolev spaces play an outstanding role in modern analysis, in particular, in the theory of partial differential equations and its applications in mathematical physics. They form an indispensable…
Function Spaces and Potential Theory
- Mathematics
- 1995
The subject of this book is the interplay between function space theory and potential theory. A crucial step in classical potential theory is the identification of the potential energy of a charge…
On certain convolution inequalities
- Mathematics
- 1972
It is proved that certain convolution inequalities are easy consequences of the Hardy-Littlewood-Wiener maximal theorem. These inequalities include the Hardy-Littlewood-Sobolev inequality for…
Green’a Functions
- Mathematics
- 1985
One approach to the solution of non-homogeneous boundary value problems is by means of the construction of functions known as Green’s functions. Historically, the concept originated with work on…
Superlinear Parabolic Problems
- MathematicsBirkhäuser Advanced Texts Basler Lehrbücher
- 2019
Preliminaries.- Model Elliptic Problems.- Model Parabolic Problems.- Systems.- Equations with Gradient Terms.- Nonlocal Problems.