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Zejia Wang

Bio: Zejia Wang is an academic researcher from Jiangxi Normal University. The author has contributed to research in topics: Uniqueness & Diffusion equation. The author has an hindex of 7, co-authored 28 publications receiving 176 citations. Previous affiliations of Zejia Wang include Northeast Normal University & Jilin University.

Papers
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Journal ArticleDOI
TL;DR: The critical global existence exponent and critical Fujita exponent are obtained by constructing various self-similar supersolutions and subsolutions of the non-Newtonian polytropic filtration equation with nonlinear boundary conditions.

45 citations

Journal ArticleDOI
TL;DR: In this paper, the critical Fujita exponents for a class of homogeneous Neumann problems of quasilinear equations with convection terms are determined and it is shown that the exponents belong to the blow-up case under any nontrivial initial data.
Abstract: In this paper, we establish the blow-up theorems of the Fujita type for a class of homogeneous Neumann problems of quasilinear equations with convection terms. The critical Fujita exponents are determined and it is shown that the exponents belong to the blow-up case under any nontrivial initial data. An interesting phenomenon is exploited such that the critical Fujita exponent even could be infinite for the model considered in the paper owing to the effect of convection.

31 citations

Journal ArticleDOI
TL;DR: In this paper, the exterior problem of the Newtonian filtration equation with nonlinear boundary sources is dealt with and the large time behavior of solutions including the critical Fujita exponent are determined or estimated.
Abstract: This paper deals with the exterior problem of the Newtonian filtration equation with nonlinear boundary sources. The large time behavior of solutions including the critical Fujita exponent are determined or estimated. An interesting phenomenon is illustrated that there exists a threshold value for the coefficient of the lower order term, which depends on the spacial dimension. Exactly speaking, the critical global exponent is strictly less than the critical Fujita exponent when the coefficient is under this threshold, while these two exponents are identically equal when the coefficient is over this threshold.

15 citations

Journal ArticleDOI
TL;DR: In this article, the p-Laplacian equation with singular sources is considered and the singularity may occur at the zero points of the solutions and on the boundary of the boundary.
Abstract: This paper is concerned with the p-Laplacian equation with singular sources which is allowed to change sign in a ball. The singularity may occur at the zero points of solutions and on the boundary. Using the upper and lower solutions method, we establish the existence of positive radial solutions for the problem considered. Copyright © 2006 John Wiley & Sons, Ltd.

13 citations

Journal ArticleDOI
TL;DR: In this article, the authors obtained the critical global existence curve and the critical Fujita curve for coupling via nonlinear boundary flux, considered by constructing the self-similar supersolutions and subsolutions.
Abstract: This paper is concerned with the porous medium equations for coupling via nonlinear boundary flux; we obtain the critical global existence curve and the critical Fujita curve for the problem, considered by constructing the self-similar supersolutions and subsolutions.

11 citations


Cited by
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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.

108 citations

01 Jun 1985
TL;DR: A survey of mathematical research in the physical and biological sciences can be found in this article, with a focus on partial differential equations, Parabolic and elliptic equations, Diffusion processes, Convective systems, Nonlinear waves, Free boundary problems.
Abstract: : This report summarizes mathematical research in the physical and biological sciences. Topics include: Partial differential equations; Parabolic and elliptic equations; Diffusion processes; Convective systems; Nonlinear waves; Free boundary problems.

91 citations

01 Sep 2004
TL;DR: A short treatise as discussed by the authors presents a concise history of the study of solid tumour growth, illustrating the development of mathematical approaches from the early decades of the twentieth century to the present time.
Abstract: A miscellany of new strategies, experimental techniques and theoretical approaches are emerging in the ongoing battle against cancer. Nevertheless, as new, ground-breaking discoveries relating to many and diverse areas of cancer research are made, scientists often have recourse to mathematical modelling in order to elucidate and interpret these experimental findings. Indeed, experimentalists and clinicians alike are becoming increasingly aware of the possibilities afforded by mathematical modelling, recognising that current medical techniques and experimental approaches are often unable to distinguish between various possible mechanisms underlying important aspects of tumour development. This short treatise presents a concise history of the study of solid tumour growth, illustrating the development of mathematical approaches from the early decades of the twentieth century to the present time. Most importantly these mathematical investigations are interwoven with the associated experimental work, showing the crucial relationship between experimental and theoretical approaches, which together have moulded our understanding of tumour growth and contributed to current anti-cancer treatments. Thus, a selection of mathematical publications, including the influential theoretical studies by Burton, Greenspan, Liotta et al., McElwain and co-workers, Adam and Maggelakis, and Byrne and co-workers are juxtaposed with the seminal experimental findings of Gray et al. on oxygenation and radio-sensitivity, Folkman on angiogenesis, Dorie et al. on cell migration and a wide variety of other crucial discoveries. In this way the development of this field of research through the interactions of these different approaches is illuminated, demonstrating the origins of our current understanding of the disease.

39 citations

Journal ArticleDOI
TL;DR: 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.

31 citations

Journal ArticleDOI
TL;DR: In this article, the critical blow-up and extinction exponents for the non-Newton polytropic filtration equation were analyzed and two critical exponents q1,q2 2 (0,+1) with q1 < q2 were revealed.
Abstract: This paper deals with the critical blow-up and extinction ex- ponents for the non-Newton polytropic filtration equation. We reveals a fact that the equation admits two critical exponents q1,q2 2 (0,+1) with q1 < q2. In other words, when q belongs to dierent intervals (0,q1),(q1,q2),(q2,+1), the solution possesses complete dierent prop- erties. More precisely speaking, as far as the blow-up exponent is con- cerned, the global existence case consists of the interval (0,q2). However, when q 2 (q2,+1), there exist both global solutions and blow-up so- lutions. As for the extinction exponent, the extinction case happens to the interval (q1,+1), while for q 2 (0,q1), there exists a non-extinction bounded solution for any nonnegative initial datum. Moreover, when the critical case q = q1 is concerned, the other parameter ‚ will play an im- portant role. In other words, when ‚ belongs to dierent interval (0 ,‚1) or (‚1,+1), where ‚1 is the first eigenvalue of p-Laplacian equation with zero boundary value condition, the solution has completely dierent properties.

27 citations