Journal ArticleDOI
Large time behaviour of solutions to a class of quasilinear parabolic equations with convection terms
TLDR
In this paper, the authors investigated the large time behavior of solutions to the exterior problems of a class of quasilinear parabolic equations with convection terms and established the critical Fujita exponents and blow-up theorems of the Fujita type for both homogeneous Neumann and Dirichlet problems.Abstract:
In this paper, we investigate the large time behaviour of solutions to the exterior problems of a class of quasilinear parabolic equations with convection terms. We establish the critical Fujita exponents pc and blow-up theorems of the Fujita type for both homogeneous Neumann and Dirichlet problems. In particular, it is shown that the critical p = pc belongs to the blow-up case under any nontrivial initial data. An interesting phenomenon is exploited that the critical Fujita exponent pc could even be infinite for the considered model because of the nonlinear convection.read more
Citations
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Journal ArticleDOI
Cauchy problems of semilinear pseudo-parabolic equations ✩
TL;DR: In this article, it was shown that there still exist the critical global existence exponent and the critical Fujita exponent for pseudo-parabolic equations and these two critical exponents are consistent with the corresponding semilinear heat equations.
Journal ArticleDOI
Large Time Behavior of Solutions to Semilinear Parabolic Equations with Gradient
TL;DR: In this article, the authors investigated the large time behavior of solutions to the Cauchy problem of a class of semilinear parabolic equations with gradient and established the blowing-up theorem of Fujita type, and formulated the critical Fujita exponent by the spacial dimension and the behavior of the coefficient of the gradient term at?.
Journal ArticleDOI
Global existence and blow-up of solutions for a Non-Newton polytropic filtration system with special volumetric moisture content
TL;DR: It is proved that the solution of a doubly degenerate parabolic system with special volumetric moisture content either exists globally or blows up in finite time.
Journal ArticleDOI
Blow-up theorems of Fujita type for a semilinear parabolic equation with a gradient term
TL;DR: In this paper, the existence and non-existence of global solutions to the Cauchy problem of a semilinear parabolic equation with a gradient term was investigated and the blow-up theorems of Fujita type were established.
Journal ArticleDOI
Critical fujita exponent for a fast diffusive equation with variable coefficients
TL;DR: In this paper, the positive solution to a Cauchy problem in R N of the fast diffusive equation with nontrivial, nonnegative initial data was considered and it was shown that there exist both global and non-global solutions to the problem.
References
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Book
Linear and Quasilinear Equations of Parabolic Type
TL;DR: In this article, the authors considered a hyperbolic parabolic singular perturbation problem for a quasilinear equation of kirchhoff type and obtained parameter dependent time decay estimates of the difference between the solutions of the solution of a quasi-linear parabolic equation and the corresponding linear parabolic equations.
MonographDOI
Linear and Quasi-linear Equations of Parabolic Type
TL;DR: In this article, the authors introduce a system of linear and quasi-linear equations with principal part in divergence (PCI) in the form of systems of linear, quasilinear and general systems.
Journal ArticleDOI
The role of critical exponents in blowup theorems
TL;DR: In this article various extensions of an old result of Fujita are considered for the initial value problem for the reaction-diffusion equation u_t =Delta u + u^p in $R^N with nonnegative initial values.
Journal ArticleDOI
Existence and non-existence of global solutions for a semilinear heat equation
TL;DR: In this paper, the existence and non-existence of global solutions and the L petertodd p blow-up of non-global solutions to the initial value problem were studied under mild technical restrictions.
Journal ArticleDOI
The Role of Critical Exponents in Blow-Up Theorems: The Sequel
Keng Deng,Howard A. Levine +1 more
TL;DR: In this paper, the authors revisited the literature since 1990 and showed that for positive solutions, the initial value problem does not have any nontrivial, non-negative solution existing on R N ǫ×ǫ[0,ǫ∞] (a global solution), whereas if pǫ>ǫ p c, there exist global, small data, positive solutions as well as solutions which are non-global.