<abstract xmlns="http://www.w3.org/1999/xhtml">The uniqueness of classical solutions to inverse parabolic semilinear problems together with nonlocal initial conditions with integrals, for the operator <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_2353737XCT.17.138-6889_eq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><munderover><mo>∑</mo><mrow><mi>i</mi><mo>,</mo><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mrow><mfrac><mo>∂</mo><mrow><mo>∂</mo><msub><mrow><mi>x</mi></mrow><mi>i</mi></msub></mrow></mfrac><mrow><mo>(</mo><mrow><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mrow><mo>(</mo><mrow><mi>x</mi><mo>,</mo><mi>t</mi></mrow><mo>)</mo></mrow><mfrac><mo>∂</mo><mrow><mo>∂</mo><msub><mrow><mi>x</mi></mrow><mi>j</mi></msub></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mo>+</mo><mi>v</mi><mrow><mo>(</mo><mrow><mi>x</mi><mo>,</mo><mi>t</mi></mrow><mo>)</mo></mrow><mo>-</mo><mfrac><mo>∂</mo><mrow><mo>∂</mo><mi>t</mi></mrow></mfrac><mo>,</mo></mrow></math><tex-math>\sum\limits_{i,j = 1}^n {{\partial \over {\partial {x_i}}}\left( {{a_{ij}}\left( {x,t} \right){\partial \over {\partial {x_j}}}} \right)} + v\left( {x,t} \right) - {\partial \over {\partial t}},</tex-math></alternatives></inline-formula>, <italic>x</italic>=(<italic>x</italic>1,..., <italic>xn</italic>), in the cylindrical domain <italic>D</italic>:= <italic>D</italic>0×(<italic>t</italic>0, <italic>t</italic>0+<italic>T</italic>) ⊂ℜ<italic>n</italic>+1, where <italic>t</italic>0∈ℜ, 0 &lt; <italic>T</italic> &lt;∞ are studied. The result consists in the introduction of nonlocal conditions with integrals.</abstract>

The uniqueness of classical solutions to inverse parabolic semilinear problems together with nonlocal initial conditions with integrals, for the operator ∑i,j=1n∂∂xi(aij(x,t)∂∂xj)+v(x,t)-∂∂t,\sum\limits_{i,j = 1}^n {{\partial \over {\partial {x_i}}}\left( {{a_{ij}}\left( {x,t} \right){\partial \over {\partial {x_j}}}} \right)} + v\left( {x,t} \right) - {\partial \over {\partial t}},, x=(x1,..., xn), in the cylindrical domain D:= D0×(t0, t0+T) ⊂ℜn+1, where t0∈ℜ, 0 < T <∞ are studied. The result consists in the introduction of nonlocal conditions with integrals.

Uniqueness of Solutions to Inverse Parabolic Semilinear Problems under Nonlocal Conditions with Integrals

Institute of Mathematics, Faculty of Physics, Mathematics and Computer Science

Institute of Electrical Engineering and Computer Science, Faculty of Electrical and Computer Engineering

Technical Transactions

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The uniqueness of classical solutions to inverse parabolic semilinear problems together with nonlocal initial conditions with integrals, for the operator...

Uniqueness of Solutions to Inverse Parabolic Semilinear Problems under Nonlocal Conditions with Integrals

Published Online: May 26, 2020

Page range: 165 - 175

DOI: https://doi.org/10.4467/2353737XCT.17.138.6889

Keywords
inverse problems, parabolic problems, semilinear equation, nonlocal condition with integral, cylindrical domain, uniqueness of solutions

© 2020 Ludwik Byszewski et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 Public License.

Uniqueness of Solutions to Inverse Parabolic Semilinear Problems under Nonlocal Conditions with Integrals

Published Online: May 26, 2020

Page range: 165 - 175

DOI: https://doi.org/10.4467/2353737XCT.17.138.6889

Keywordsinverse problems, parabolic problems, semilinear equation, nonlocal condition with integral, cylindrical domain, uniqueness of solutions

© 2020 Ludwik Byszewski et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 Public License.

Keywords
inverse problems, parabolic problems, semilinear equation, nonlocal condition with integral, cylindrical domain, uniqueness of solutions