1.广东工业大学数学与统计学院,广东 广州 510520
2.中山大学数学学院,广东 广州 510275
3.南方医科大学口腔医院,广东 广州 510280
胡蝶(1997年生),女;研究方向:偏微分方程;E-mail:1483358628@qq.com
卫雪梅(1972年生),女;研究方向:偏微分方程;E-mail:wxm_gdut@163.com
冯兆永(1977年生),男;研究方向:偏微分方程;E-mail:fzhaoy@mail.sysu.edu.cn
纸质出版日期:2021-11-25,
网络出版日期:2021-09-27,
收稿日期:2021-01-16,
录用日期:2021-04-24
扫 描 看 全 文
胡蝶,卫雪梅,冯兆永等.具有Robin自由边界的坏死核双曲型肿瘤生长模型的定性分析[J].中山大学学报(自然科学版),2021,60(06):150-160.
HU Die,WEI Xuemei,FENG Zhaoyong,et al.Qualitative analysis of necrotic hyperbolic tumor growth model with Robin free boundary[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2021,60(06):150-160.
胡蝶,卫雪梅,冯兆永等.具有Robin自由边界的坏死核双曲型肿瘤生长模型的定性分析[J].中山大学学报(自然科学版),2021,60(06):150-160. DOI: 10.13471/j.cnki.acta.snus.2021A006.
HU Die,WEI Xuemei,FENG Zhaoyong,et al.Qualitative analysis of necrotic hyperbolic tumor growth model with Robin free boundary[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2021,60(06):150-160. DOI: 10.13471/j.cnki.acta.snus.2021A006.
研究了一个具有坏死核的双曲型肿瘤生长的Robin自由边界问题。该模型包含了一个描述营养物浓度变化的椭圆型方程,一个描述肿瘤半径的常微分方程和三个分别描述增殖细胞,休眠细胞和死亡细胞演化的一阶非线性双曲偏微分方程。通过特征线方法和
<math id="M1"><mi mathvariant="normal">B</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">h</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49507435&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49507444&type=
9.31333351
2.28600001
不动点定理证明了该模型整体解的存在唯一性。同时证明了当
<math id="M2"><msub><mrow><mi>K</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">0</mn></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49507452&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49507447&type=
8.89000034
3.21733332
时,
<math id="M3"><munder><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">m</mi></mrow><mrow><mi>t</mi><mo>→</mo><mo>+</mo><mi mathvariant="normal">∞</mi></mrow></munder><mi>R</mi><mfenced separators="|"><mrow><mi>t</mi></mrow></mfenced><mo>=</mo><mo>+</mo><mi mathvariant="normal">∞</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49507473&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49507456&type=
20.15066719
4.06400013
.
The necrotic hyperbolic tumor growth model with Robin free boundary is studied.The model contains an elliptic equation describing the diffusion of nutrient in the tumor,an ordinary differential equation describing tumor radius,and three nonlinear first-order hyperbolic partial differential equations describing the evolution of proliferating cells,quiescent cells and dead cells,respectively.By applying the characteristic theory of hyperbolic equations and the Banach fixed point theorem,the existence and uniqueness of the global solution of the model are proved.It is proven that
<math id="M4"><munder><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">m</mi></mrow><mrow><mi>t</mi><mo>→</mo><mo>+</mo><mi mathvariant="normal">∞</mi></mrow></munder><mi>R</mi><mfenced separators="|"><mrow><mi>t</mi></mrow></mfenced><mo>=</mo><mo>+</mo><mi mathvariant="normal">∞</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49507465&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49507461&type=
23.19866753
4.57200003
in the case
<math id="M5"><msub><mrow><mi>K</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">0</mn><mo>.</mo></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49507487&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49507467&type=
11.51466751
3.80999994
肿瘤生长坏死核自由边界问题整体解
tumor growthnecrotic corefree boundary problemglobal solution
BYRNE H M, CHAPLAIN M A J. Growth of nonnecrotic tumors in the presence and absence of inhibitors [J]. Mathematical Biosciences, 1995, 130(2): 151-181.
BYRNE H M, CHAPLAIN M A J. Growth of necrotic tumors in the presence and absence of inhibitors [J]. Mathematical Biosciences, 1996, 135(2): 187-216.
崔尚斌. 肿瘤生长的自由边界问题[J]. 数学进展, 2009, 38(1): 1-18.
FRIEDMAN A, REITICH F. Analysis of a mathematical model for the growth of tumors [J]. Journal of Mathematical Biology, 1999, 38(3): 262-284.
CUI S, FRIEDMAN A. Analysis of a mathematical model of the effect of inhibitors on the growth of tumors [J]. Mathematical Biosciences, 2000, 164(2): 103-137.
CUI S, FRIEDMAN A. A hyperbolic free boundary problem modeling tumor growth [J]. Interfaces & Free Boundaries, 2003, 5(2): 159-181.
CUI S. Analysis of a mathematical model for the growth of tumors under the action of external inhibitors [J]. Journal of Mathematical Biology, 2002, 44(5): 395-426.
CUI S. Analysis of a free boundary problem modeling tumor growth [J]. Acta Mathematica Sinica, 2005, 21(5): 1071-1082.
卫雪梅, 崔尚斌. 一个肿瘤生长自由边界问题解的整体存在性和唯一性[J]. 数学物理学报, 2006, 26(1): 1-8.
卫雪梅, 崔尚斌. 一个肿瘤生长自由边界问题解的渐近性态[J]. 数学物理学报, 2007, 27(4): 648-659.
CUI S B, WEI X M. Global existence for a parabolic-hyperbolic free boundary problem modelling tumor growth [J]. Acta Mathematicae Applicatae Sinica (English series), 2005, 21(4): 597-614.
CUI S, FRIEDMAN A. Analysis of a mathematical model of the growth of necrotic tumors [J]. Journal of Mathematical Analysis and Applications, 2001, 255(2): 636-677.
WEI X. Global existence for a free boundary problem modelling the growth of necrotic tumors in the presence of inhibitors [J]. International Journal of Pure and Applied Mathematics, 2006, 28(3): 321-338.
FRIEDMAN A, LAM K Y. Analysis of a free-boundary tumor model with angiogenesis [J]. Journal of Differential Equations, 2015, 259(12): 7636-7661.
SHEN H, WEI X. A qualitative analysis of a free boundary problem modeling tumor growth with angiogenesis [J]. Nonlinear Analysis: Real World Applications, 2019, 47: 106-126.
ZHUANG Y, CUI S. Analysis of a free boundary problem modeling the growth of multicell spheroids with angiogenesis [J]. Journal of Differential Equations, 2018, 265(2): 620-644.
ZHENG J, CUI S. Analysis of a tumor model free boundary problem with action of an inhibitor and nonlinear boundary conditions [J]. Journal of Mathematical Analysis and Applications, 2021, 496(1): 124793.
沈海双, 卫雪梅, 刘成霞, 等. 具有第三边界坏死核肿瘤数学模型稳态解的存在唯一性[J]. 中山大学学报(自然科学版), 2018, 57(5): 140-144.
XU S, SU D. Analysis of necrotic core formation in angiogenic tumor growth [J]. Nonlinear Analysis: Real World Applications, 2020, 51: 103016.
SONG H, HU W, WANG Z. Analysis of a nonlinear free-boundary tumor model with angiogenesis and a connection between the nonnecrotic and necrotic phases [J]. Nonlinear Analysis: Real World Applications, 2021, 59: 103270.
0
浏览量
0
下载量
0
CSCD
关联资源
相关文章
相关作者
相关机构