75 research outputs found
Well-posedness of the Viscous Boussinesq System in Besov Spaces of Negative Order Near Index
This paper is concerned with well-posedness of the Boussinesq system. We
prove that the () dimensional Boussinesq system is well-psoed for
small initial data () either in
or in
if
, and , where
(, , )
is the logarithmically modified Besov space to the standard Besov space
. We also prove that this system is well-posed for small initial
data in
.Comment: 18 page
Asymptotic expansions of the solutions of the Cauchy problem for nonlinear parabolic equations
Let be a solution of the Cauchy problem for the nonlinear parabolic
equation and
assume that the solution behaves like the Gauss kernel as . In
this paper, under suitable assumptions of the reaction term and the initial
function , we establish the method of obtaining higher order
asymptotic expansions of the solution as . This paper is a
generalization of our previous paper, and our arguments are applicable to the
large class of nonlinear parabolic equations
Successfully treated synchronous double malignancy of the breast and esophagus: a case report
<p>Abstract</p> <p>Introduction</p> <p>The incidence of multiple primary cancers is reported to be between 0.3% and 4.3%. The second primary lesion is identified either simultaneously with the primary lesion (synchronous) or after a period of time (metachronous). Few cases of metastasis of breast carcinoma to the esophagus and vice versa have been reported in the past.</p> <p>Case presentation</p> <p>We report an extremely rare case of a 55-year-old Indian woman who had carcinomas in both the esophagus and the breast simultaneously. She was treated successfully using combined modalities of surgery, chemotherapy and radiation therapy.</p> <p>Conclusion</p> <p>Cases of synchronous double malignancies can be treated by dealing with the malignancy in the two sites as independent carcinomas. We have to take into consideration the total dose of radiation to a critical organ as well as the effect of the total dose of toxic chemotherapeutic drugs on our patient.</p
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