Journal of the Ramanujan Mathematical Society

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On The Cauchy Problems for Parabolic Equations


Affiliations
1 Instituto Tecnologico Y De Estudios Superiores De Menterrey, Campus Edo, De Mexico, Division De Graduados E Investigation, Km 4 Carretera Lago De Guadalupe, Atizapan De Zaragoza, Edo de Mexico C.P. 54500, Mexico
2 Havana Pedafofical Institute, Ciudad Libertad, Marianao, Habana, Cuba
     

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We consider the Cauchy problem for a linear parabolic equation in a layer. Under the assumption of general Holder continuity of the coefficients of the equation with respect to space variables only, we establish the existence and uniqueness of the solution.

This result is applied to obtain the solvability of the Cauchy problem for a nonlinear parabolic equation in general Holder anisotropic spaces.

The second derivatives with respect to x of the corresponding solutions satisfy the general Holder condition with respect to the space variables and with respect to the time.


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  • On The Cauchy Problems for Parabolic Equations

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Authors

Martin Lopez Morales
Instituto Tecnologico Y De Estudios Superiores De Menterrey, Campus Edo, De Mexico, Division De Graduados E Investigation, Km 4 Carretera Lago De Guadalupe, Atizapan De Zaragoza, Edo de Mexico C.P. 54500, Mexico
Justo Che Soler
Havana Pedafofical Institute, Ciudad Libertad, Marianao, Habana, Cuba

Abstract


We consider the Cauchy problem for a linear parabolic equation in a layer. Under the assumption of general Holder continuity of the coefficients of the equation with respect to space variables only, we establish the existence and uniqueness of the solution.

This result is applied to obtain the solvability of the Cauchy problem for a nonlinear parabolic equation in general Holder anisotropic spaces.

The second derivatives with respect to x of the corresponding solutions satisfy the general Holder condition with respect to the space variables and with respect to the time.